The short answer is, that we don’t know exactly. This question cannot be answered accurately with the information that is currently publicly available. However, we do know that there are hundreds of organisations licensed to use animals for research and scientific purposes in Australia, and there are dogs and cats (as well as many other species) that could be rehomed that are currently euthanised at the conclusion of research.

The long answer is that we can use the available data to derive a rough idea of:
1. the number of animals nationally that could be available, but not necessarily suitable, for rehoming.
2. the number of animals in NSW only that could be available, but not necessarily suitable, for rehoming.

1. Number of animals in Australia (NSW, VIC, QLD, TAS and WA only) that could be available, but not necessarily suitable, for rehoming

The latest available figures, for 2017, show that the percentage of animals used for non-observational[1] procedures in Australia, involving varying levels of invasiveness and challenge but not resulting in death was 11.5% (2.31 million animals) from a total of 20,160,469[2] used for scientific purposes. This is based on data from five states of Australia but includes the largest user states. In theory, it is animals from this group that could potentially be available, but not necessarily suitable, for rehabilitation and rehoming. This includes 993,794 animals from Victoria and 677,038 animals from NSW[3].
It should be noted that the overall total in 2017 was skewed by two unusually large studies that involved minor impact on animals involving some 13.2 million animals. If these animals are removed from the overall national total (the data from five states) then the percentage of animals that could potentially be available for rehoming rises to 33%.
Of the total for the five states recorded, across all types of research including observational studies, the number of mice was 1,471,837, the number of rats was 124,472, the number of guinea pigs and rabbits was 13,421, the number of dogs was 11,368 and the number of cats was 2,587.
Around 1.5% (306,504 animals) of the animals recorded across the five states were involved in genetic modification, which are unable to rehomed.
It should also be noted that this information relates to only five states of Australia. It is estimated that other states/territories could account for a further 599,242 animals.[5]

2. Number of animals in NSW that could be available, but not necessarily suitable, for rehoming

What do we mean by ‘not necessarily suitable for rehoming’? Many companion animals such as dogs and cats are included in statistics of animals used for scientific purposes although they may only be consulting at university-based veterinary clinics and do not belong to the university. There may be other animals that while owned by the research facility, may not have a suitable temperament or physical or psychological condition to be rehomed.
What the latest figures (2018)[6] from NSW show is that there were large numbers of farm animals such as poultry, pigs, sheep and cattle being used for research purposes in NSW in a variety of procedures. Aside from the largest groups – rats, mice, amphibians and aquatic species – there were a number of other animals that may be suitable for rehoming as shown in the table. These included captive native and exotic birds, cats, dogs, rabbits and guinea pigs, and horses.
It can be estimated that up to 3329 dogs and 986 cats in 2018 could have been available for rehoming. However, a proportion of these would be animals being treated at university-based veterinary clinics as mentioned above that belong to members of the public.
In addition, dogs and cats may be bred in research establishments and remain involved in research until the age of 7 or 8. This means that they may be counted as part of studies each year, but may not be considered for “retirement” or rehoming that year. So, for 1,000 dogs reportedly used in research in a year that do not die as part of the process, there may only be a small percentage that are ready for rehoming.
Anecdotally, it has been suggested there may be around 1,000 dogs available for rehoming in NSW each year and a lesser number of cats, around 500. However, these figures are only educated guesses.

Click on the image below to view the table: NSW animal use in research in 2018 by animal type, research category and selected procedure categories [animals that may be suitable to be rehomed as pets and companions have been highlighted]

The reasons why we cannot provide an accurate answer to the question of the exact numbers of animals moving through research establishments are as follows:

• Not all Australian states and territories publicly release data on animal useage for scientific purposes. The data used in this post comes from NSW, Victoria, Queensland, Tasmania and WA. This is significant given that the majority of research involving animals occurs in NSW and Victoria.
• Australian research institutions do not provide information on the numbers and types of animals that are suitable for rehoming specifically. From the calendar year 2018, research establishments in NSW were invited to report on the fate of animals but the only respondents were those involved in large-scale observational studies, where the animals are often living in the wild. From calendar year 2019, research establishments have been required to report on the fate of dogs and cats. These figures should be available for the first time later in 2020 and will provide a good guideline to estimating the demand for rehoming of these species in NSW.
• Australian research institutions provide aggregated figures to state governments on their use of animals by species and the category of procedure. The only state which provides data that cross references species with the type of procedure involved is New South Wales, which enables analysis of approximate numbers and types of animals that may be suitable for rehoming in that state. For example, we can ascertain the number of mice that were subject to procedures that did not result in their death or involve genetic modification. Note, genetically modified animals are not suitable for rehoming as they must be kept in secure, specialist facilities by law.

Notes on the table:
Data includes procedure categories: 1, 3, 4, 5, 6, 7 only. It excludes procedure categories 2, 8 & 9 which involve death of the animal or production of genetically modified animals
Data excludes animals used for the purposes of stock breeding; stock maintenance; and environmental study
Descriptions of procedure categories:
Observation with minor interference – included in table
Animal unconscious without recovery – not included in table
Minor conscious intervention – included in table
Minor surgery with recovery – included in table
Major surgery with recovery – included in table
Minor physiological challenge – included in table
Major physiological challenge – included in table
Death as an endpoint – not included in table
Production of genetically modified animals – not included in table
Where a cell is left empty it indicates zero animals were reported
Source: Animal Research Review Panel Annual Report 2018, NSW Department of Primary Industries, 2020

References:
[1] Animals involved in observational studies are not included where they are considered non-invasive as they are mostly conducted with free-living or sanctuary populations
[2] http://www.humaneresearch.org.au/statistics/statistics_2017
[3] http://www.humaneresearch.org.au/statistics/statistics_2017
[4] http://www.humaneresearch.org.au/statistics/statistics_2017
[5] http://www.humaneresearch.org.au/statistics/statistics_2017
[6] Animal Research Review Panel Annual Report 2018, NSW Department of Primary Industries, 2020