Before you jump into rooting, consider that doing so may prevent you from accessing Amazon streaming video. I have two Kindle Fire devices (one of which I plan to disassemble, drop and scratch test) and the one that I rooted and installed Google Android Market on doesn't play videos anymore.
Buttons are disabled with message (that device is no longer configured correctly to play videos) and I should contact CS. I did the rep doesn't have an idea about what is going on so he passed my ticket to tier-2. I'm still waiting on results.
The other Kindle that I didn't root can still access videos without any problems.