What kind of power source would I need? I'm thinking it might be able to run off a 3V lithium battery. It would probably generate about 1 mW. Would I need something bigger?
That's a pretty small signal - I've seen micro power transmitters on lower frequencies that had 100mW into the final amp and radiated 40microwatts at the fractional wavelength antenna. The range of that transmitter was about 80ft with the available receiver.
The challenge will be to make your receiver sensitive enough to pick out your signal from the natural background noise. You haven't mentioned what kind of signal you plan to transmit; however, I would assume you plan to "chirp" modulate the RF, or use some sort of pulsed signal. A pulse is easier to pick out of the noise than a steady RF carrier. Additionally, FM is more likely to work for you than AM simply because of the abundance of AM noise around us in the world.
1mW is a pretty challenging power level. You're just going to have to experiment to see if you can make it work. The key to locating a low power transmitter in the range you propose is in the sensitivity of the receiver.