Honestly, she sounds like a cool character to hang out with. Definitely worth considering locking down.
Sorry, I'm not a single dad. Prepping for marriage though.
In all randomness, have you considered having her hang out with your kid then asking your kid about what the kid thinks of the new lady? Don't mince words. Ask direct questions (but only when you're far more comfortable and ready of going next step with date lady). Kids can adapt pretty easily, but the trick is to get the kid to want/need to adapt in a proper way first. Some kids get mad they lose you (because they were the centre of the world of a single parent, then 2nd place. It irks them) and as a result dislike the other parent solely for this reason even if everything else is fine. Easing in might help, and full communication between significant other and existing kids probably is very important.
A lot of family break downs are due to communication and/or finances. I'm thinking not just between spouses, but between kids and parents too.
And... clarify semantics with the date lady. Apparently there are some women out there who want kids and families but don't want to give birth (ie: kids via adoption). Her hinting she wants her own family might not necessarily mean making more kids together, it means she wants to take children under her wing (Odd IRL story of a friend of a friend as bizarre as it sounds). Or it might also potentially mean she wants someone to pop the question quickly (someone I know, possibly me
). You might want to chat and clarify which one rather than assume (but might be a chat to do closer to engagement than right away).
Good luck.