How would you iniciate the talk?

So me and my bf have been dating for 3 months now, I know it's a short time but nowadays you don't really care about the time but the person... we get along just fine, we both have goals and plans together, we've talked about doing a life together and I sometimes feel like he's about to ask me to move in together, although sometimes feel like it can take longer. I'm not desperate but I'm ready.

Happens that my family and I have been having a few problems, where things get worse instead of getting better, we've thought about moving out of the area where we are just to start off fresh and make some changes. When I woke up this morning my mom told me that she needed to talk to my bf about taking me with him (wich I reply that is something he and me have to talk) she said she's my mom and that she wants the best for me, and wants me to be safe, we live in florida, and she's planing to move to Boston after my brother and I get our lives together so she can move over there in peace. I'm a nursing student currently working at mcdonalds (and looking for a better job as I move forward in my carreer) I'm saving money to buy a car or just waiting for the income tax return to get me one out of the dealership since mine broke down few weeks ago. My bf is a fighterfire paramedic and lives by himself. I know about people moving in the first month of knowing each other but I'm kinda scare of bringing the situation in to my bf, As we've talked about moving in together sometime I'm sure that we will try to work things out and see how we split everything between us.

My question is any advices of how to bring this up to him? Would it look good if I did? Would him be turn off by me asking first?

Any advices will be appreciated. Thank you all ❤️