I think the female will go back into heat about eight weeks after birth, maybe sooner or later. I don't think her giving birth prematurely affects when the mother goes into heat again. It is best to wait to spay her after the kittens are weaned.
Yes, I meant days. My female had kittens in August, but they all died. It was maybe five days after when she went back into heat, I'm not sure. It may be longer for some females. But from what I have gathered it's not very long before she goes into heat again.
We have a local clinic that does spay & neuter for reduced prices and they were able to give me an appointment in early December. The lady said that since the birth had been very recent she may still be storing up milk and its best to wait till that goes down before doing the surgery. But she said that was the first available appointment.