Is it normal to be 20 and really want a baby?

I'm not saying I'm going to do it, I'm not quite ready to take care of a little one and sacrifice the plans I have in place for the next couple years but holy crap I have baby brain all day every day. About 13 months ago I had to abort a pregnancy at 8 weeks (there were serious health concerns for both me and the fetus), and for the past 4 months all I can think of is starting a family. I know my boyfriend still thinks about it and I know he feels the same way, though I don't think he thinks about it quite as much as I do. I also moved away from home to go to school about 5 months ago and in doing so had to leave my cat with my mom. Do you think, when I move out into an apartment and can bring my cat with me, it will get better (even if the urge doesn't go away)? But are those feelings normal after what I went through and with my age and all that?

Also, and I think this is more a question for the ladies to just answer in the comments, a lot of the desire I'm feeling right now is for the actual pregnancy, like 65% of the time I'm thinking of pregnancy and the other 35% it's actually the baby. Have you had similar experiences or feelings?