No, she should stay out of Washington's infested swamp and run for re-election as Governor. She has a better chance of retaining her Governor role than being one out of a 100. In 2012 she'll have a solid six years under her belt. The same gubernatorial experience Bush had in TX and she'll be more than ready to run on her own.
And she'll have her own team of advisers and a strong support base of conservatives. Palin is the front-runner now.
People keep saying this but it is a crazy idea - I don't know if she can "appoint herself" legally but that would wreck her "reformer" credibility forever. It would be portrayed as worse than the nepotism of appointing a family member, appointing yourself, and anyway that was one of the issues that undermine Murkowski when he was AK Governor -- he appointed his daughter Lisa to fill the other US Senate seat.
Anyway, I don't see any merit in her rushing to become one of 100 Senators, even if she were elected to the seat. Far better to serve out her term as Governor and build her record of accomplishment there. She's young, if anything she should be looking past 2012 unless Obama is obviously weakened politically -- she can serve 2 terms as Governor, and be ready for 2016 if 2012 is not in the cards.
This year is unusual in having a US Senator elected POTUSA, but I think that a successful Governor will always have advantages over people in Congress due to the executive experience and leadership.