"We are chocka and actually having to turn people away," said executive officer Phil Soper.
The society was only taking animals in dire circumstances, and people who had let their cat have a litter of kittens would have to find them homes themselves.
About 18 kittens, 15 dogs and puppies and 34 adult cats are in the adoption catteries and kennels, with more animals waiting to take their places.
The society could not allow the catteries and kennels to become overcrowded, and always had to keep some spaces open for rescued animals.
"It is always busy at this time of the year, but this year it has reverted back to the days of old. It is like the early '90s, with these sorts of numbers at this time of year."
Constant messages about having animals desexed and not allowing any animals to leave the society's haven unless they had been desexed had steadily reduced the numbers of unwanted kittens and puppies, and he was not sure why this year was an exception, Mr Soper said.
"It is just people being irresponsible."
The society used to give out vouchers with animals to have them desexed, but now has them desexed before they leave, to ensure it is done.
As well as unwanted animals, Christmas always brought in generous donations of pet food, for which the society was grateful, Mr Soper said.
However, this year they were running low on stocks of tinned kitten and puppy food.
They had lots of biscuits and adult tinned food, but had been buying tinned kitten and puppy food to ensure the animals had a balanced diet.
Finding homes for adult cats was always especially challenging at this time of year when people were only interested in kittens, Mr Soper said.
A recent donation to the society specifically for adult cats enabled the society to give a $50 pet shop voucher with each cat that went to a new home.
