A.S.
Closeness has nothing to do with the age and everything to do with the individual personalities and how they are raised.
I also had wanted my kids to be 3 years apart. They ended up being 4.5 years apart. While I don't have too much experience to speak of (they are 5 1/2 and 16 months right now) it seems like so far they are very close. The older one adores the younger one, though sometimes he is annoyed with him, and the younger one copies everything the older one does. They play together all the time. And they are still close enough to have sibling rivalry going on (especially the older one towards the younger one right now). I wouldn't worry.