Is it dumb to travel to the Caribbean in late Sept/early Oct?

BoBride28

So DH and I are toying with the idea of a babymoon and would love to have a beach vacation. Somewhere in the Caribbean comes to mind and the prices are usually good this time of year, but being that it's hurricane season, is it a dumb idea? I heard that Aruba is located outside of the hurricane belt, but I don't know...