you get the belt in the 3rd hatcher...
you get the belt in the 3rd hatchery after cobbs hatchery, i think that is the name. anyway it is the 3rd one you get the key for.
you get to rosewood by giving the lady in the town after the 3rd hatchery her money and her ring which you will get the key when you buy the toddsword and give it to the guy who wants it in the same town he sells pets.