Dangers of building a radio transmitter?
To cover two stories you won't need more than a watt of power. This is in the safe range and shouldn't be an issue.

Large AM radios do use a lot of power, but they're expected to cover hundreds or thousands of miles, not your application. Same for FM.

By the way, for Music and better reliability it's best to use FM. If you want to build something, you can also use chips like the ones from SiLabs:

http://www.silabs.com/products/audiovideo/fmtransmitters/Pages/default.aspx

You can of course go the more discrete route and build all from scratch, which could be a a fun endeavor.