Moving advice 🤔

So I am due September 4th. Come September I will have a 6,5, year olds and a newborn and we currently live in a one bedroom 🤦🏻‍♀️🙄 we’re already cramped in here and adding a newborn and everything they need there is just no way we can stay here. I’m planning on moving to a 2 bedroom at the end of my lease in May. But I’m think my landlord is a super sweet lady and I know she will let me go to a month to month lease. My problem is should I move at the end of my lease in May or the end of August? I’m thinking it will be best to move at the end of August that way when I pay my first month rent and deposit, September’s rent will be paid and I can pay October rent with my last check before I go on my maternity leave?

What are your guys thoughts? Or any ideas?