Fwiw op I also had an abusive relationship.
I've now been seeing someone for 5 years, we knew each other as teens.
I introduced him to my adult dc after about a year, my younger dc met him after 2, and he has only started staying over at my house the last few months.
From about 2.5 years in we would have days out together, so I could see him interacting with my kids, my older dc and him had been meeting semi regularly as well (to golf and have lunch), after these days out with my younger dc he would go home again, not back to my house.
It's bloody hard being a single mum, it's even harder after you've been in an abusive relationship, but it's taught me to be very, very cautious, I don't trust words, I trust what I can see, and after only a few months and less than 20 meet ups you haven't seen a lot.
You're going very fast, and I get that urge to jump in feet first to have a settled and stable and happy family, unfortunately you can't speed that process up.
The way I've done things has certainly been frustrating at times, now I'm 5 years in and still happy I probably could have sped things up a bit, but I didn't know how things would pan out in the first few years. Admittedly they still might not, but I've made sure there's been a solid base, nothing has been decided on a whim, and he has still stuck around and proved himself reliable and loving, so there's a huge chance that this is going to turn into moving in together when my kids are all teenagers and he has been around as a loving a stable influence in their lives for the best part of a decade.
My kids are my absolute priority, that's not to say I don't deserve happiness, but they deserve a childhood free from abuse more, that's why I left their dad.
Just take it slowly, if you think he's around for the long term then there is absolutely no rush at all.