I think you will do fine especially if you have $600 left over.
DF is the only one working atm and I'm expecting so he gets $700/week. Our rent is $360. So $340 is left for fuel for 2cars, bills and groceries a week. It's hard but we are doing it.
So I think $600 after rent for yourself and your child you should do fine.
I've got it set up so that our bills are slowly paid via automatic transfers every week so that it's easier to keep up and we don't over spend.