Aww look at the baby seems fair enough. That's a natural reaction...
my girlfriend talks about it a ton. to some extent I don't mind because it means that she really feels very serious about me and that is a good thing. at some point though it does just become burdensome and it makes the guy feel like is that all there is. Plus it can be a lot of pressure. Especially at your age (under 18?) I'm surprised a guy would stick around that long if you talk about babies as much as you say you do.
Your position is clear. You want babies. You've made that clear and he should know that is your end game. So dial back talking about it so much or you could scare him away.
If your boyfriend stopped talking about sex would you believe he didn't want it? Remember girls , you ain't daft and neither are we lol
It's fine to want babies and find them cute etc. I actually find that attractive in a woman. The only thing you want to avoid us your boyfriend feeling like you are pressuring him into having kids. If you can avoid that you can cuddle as many babies as you like.