Would this convince u, and how do u see it working out?

Basically my gfs mum is going away for two week, and has asked us to house sit, and look after my gfs lil bro, I mean like neither of us live together yet but was wondering what the protential out come of this cud be??? Also whilst I'm there how can I show her tht living with me will be a good thing??? As I really wish we'd move into together, also. We will be doing things like taking care of the bills, going out to work, and generally arranging childcare??? Also I wanna try and use this to convince her to move in with me (both in our early-mid 20s)