My age gaps are a bit reversed- 6 this month, 4.11 and 2.5 so the older two were close together. DS1 was 5 months when ds2 conceived, I had felt broody fro weeks by that pint- just waiting for the wedding to happen first!
I felt broody days after all of mine, and have done since ds3 was born, increasingly lately although I am younger at 32. However, I am not going to be able to have another for a few years yet as studying.
Would I recommend the close age gap? Absolutely. My ds1 has some problems with friendships (AS) but having ds2 means that he always has a mate. They see other kids alone in the holidays and it confuses them, they pity them in fact. They constantly express worry about my nephew who has to be an only child because of pg complications.
You have to be OK with the fighting that siblings do anyway, as I think you get more than if the gap was smaller. BUT the friendship once they get old enough is truly amazing. My two curl up together in bed at night .
I think being immediately broody is absolutely normal (well it is for me) and that such a close age gap would be fine if that's what you want. Only you can know how your other kids will react, but you'll get the nappy years over and done with quicker (a good reason to give a 4.5 yr old if anything like my ds2!).