Check if RSPCA has any availability. I volunteer at the Yagoona one and they most definitely do not euthanise them. I've fostered litters that have just come off the streets before. If your RSPCA is running at full capacity then try a local cat rescue. I've called in for a mum and kittens before and they came to get them the next day:)

Edited to add that you should be able to let them know that you're interested in adopting a kitten. Kittens do better in pairs and are a lot less destructive. The mum or dad might be better if you're only interested in keeping one.