I'm expecting my girlfriend to move on short notice
Why do you want her to move so quickly?
I've paid 2 rounds of rent in advance.
It sounds like you were being thoughtful to pay for rent for her. Does she know you expect her to move in right away or is this a surprise. A lot goes into moving and leases that can complicate matters!
I'm planning on surprising her with it.
I think that you should have talked about it sooner. It is important to give people plenty of time to prepare for a major change like this in their life.