As of yet there are no official dates. LittleBigPlanet is, at last check, coming to us sometime in October with the possibility of a beta test period before that.
As for Home, it's anybody's guess at this point. They still say "to be announced". Considering the Euro date listed is Q3 2008 we can possibly expect it at about the same time. It's all up to Sony saying "it's ready" and for the moment, they think it isn't. Kind of a good thing, really- personally, i prefer they iron out the bugs and do a proper releaee than shove it out half- assed and patch it later.