Should we move in together?

We've been dating for 4 months now and we feel like if we've known each other forever. We want to sleep and wake up next to each other. I have over protective parents who refuse to realize i am growing up and he has problems at home with his family. Im 20 and he is 23 with 2 adorable kids under 2 yrs old. We were thinking to wait until we are more financially stable then move out with a friend so rent would be bearable. I dont want to regret anything or seem as if i did a bad decision. And i want to prove my parents that i am responsible. Opinions?