Persoanlly I would say 'wait'
What is there to lose by waiting a few more months? You can continue to enjoy being together and have a full 'going out' phase which is different to the living together phase. If it fizzles out because you are not living together (and I'm not quite sure why that would happen) then it would have ended anyway, and it's good that you haven't moved in.
I think there are several things to note. You are pretty young and already divorced, as well as having had another. Long term relationship. You may think that serial living-together monogamy is a good idea, but what you are really after is 'the one' from your post. If you want to avoid this being one in a string of living together relationships, then it might be worth taking your time and making sure it is right, before launching in. As someone who is divorced, I'm sure you know how messy and difficult it is getting out of marriages and relationships where you live together. I think you need to have a bit of a sense of 'once bitten, twice shy' type thing. It might be even more important as he has children....you need to think of them too, as does he. He particularly should be wary of introducing new people into their lives too quickly, and the fact he is willing to do this so soon, does ring warning bells with me, in terms of his priorities.
None of this is to say that this relationship cannot or won't work.
Personally, I think that drifting into living together,without having had a proper conversation about long term commitment is problematic. I have known lots of women who have done this pretty quickly, seeing it as a low level commitment which could be ended if need-be. And then these relationships continued, and they found they had been living together for 6 years bout never really found out if they were on the same page about having children, finances, caring for elderly parents and other dull but important topics that you need to be on the same page about with a life partner. And then it was difficult to have those conversations and even more difficult when they found they weren't on the same page, to get out of those relationships. So I think it is worth waiting and actually people should have a pretty strong commitment to a future together before moving in together. I think it gives a much better basis for success.
I realise this doesn't fit with many people's approach these days, which is to move in together pretty quickly. Clearly,some of these relationships work and become very long term. But many don't and there is much hurt involved.
So I ask you the question, what have you to lose by waiting say another 6 months? If it all feels so urgent, ask yourself why that should be so, because waiting a while shouldn't be a problem. And ask him the same question too. Use the time to see if you are fully on the same page about the important things in life, rather than just hoping you are. You are in the early throes of love or lust and tbh your judgement probably isn't totally rational,with the greatest respect.