I have 2 kittens: the male is 4 months old and the female is slightly under 2 months old.
My vet has informed us that if I were to have one neutered I should wait until 6 months of age. Additionally, they recommended that we have the female spayed, and therefore able to leave the male intact.
Can I allow them to play together unattended for another 4 months without having to worry about them possibly having a litter?
In short: That might be too long, try to reschedule the spaying to an earlier date.
The male will mature earlier than he female, but as long as the female isn't mature as well, they cannot reproduce.
The average age of sexual maturity for female cats is 5 - 6 months, but that also depends on the season. If you live in the northern hemisphere where spring is on its way, your cat might be in heat (or have been in heat) in 4 months. You should spay her before that happens. It's a bit of a gamble...
It is possible to safely spay a cat at 4 - 5 months of age Source: bluecross.org, PetMD and todaysveterinarypractice.com, but they must be big enough for the vet to clearly see the the reproductive organs. It's ideal to spay the cat before she goes into heat, because during a heat the reproductive organs become engorged with blood which makes the procedure more risky.
The signs that your cat is going into heat are very obvious, but still easy to miss at the very beginning:
If your cat goes into heat before you spay her, make sure to always keep at least 2 closed doors between her and the male and keep all windows completely shut in the room she's in.
There are medications to prevent a heat, as described in this answer.
You should think about neutering your tomcat as well. Not only does that potentially reduce the number of stray cats he could sire, but it also prevents undesirable behavior like marking walls or furniture with urine. You can read more about the problems of keeping an unneutered tomcat in this question.
