In a word: No.
Ms. Kennedy is a recent inductee in the world of politics; she has not held a legislative branch position. Mr. Bush is a little more understandable; he was the (strangely) popular Governor of Florida--I wouldn't vote for him, but he at least is sort of qualified. But it's an executive branch position. Same goes for Mr. Biden, who was an Attorney General and is currently serving in Iraq.
None of these people have served in the legislative branch. The Senate is not just "a legislative position"; it's the highest office of legislature in the country. Now, I don't think that's necessarily required. But. Would we be considering these people if they weren't in a wealthy family? I think this goes especially for Caroline Kennedy, but the same reservations exist in my mind for Biden and Bush. Kennedy is a third generation political name; Biden and Bush are second generations.
Stop with this madness, before Jenna Bush or Chelsea Clinton run for office.