I know this conversation is a bit old, but small ferrite loop antennas can transmit after a fashion. A few years ago, I cajoled our son into a radio project for the science fair. We made a part 15 transmitter, working at the top of the AM broadcast band, and tested some different antennas. One of these was a ferrrite rod resonated with a variable cap, and a small winding coupling to it from the transmitter. It worked quite well, although not as well as a coil loaded 10ft vertical. We were trying to stick within the spirit of Part 15 regulations for power and antenna size. Part of this was that with tight coupling, the antenna pulled the transmitter oscillator, so it was hard to get it perfectly on tune for full efficiency.
I mean to test this again one day, just for fun, using some more stable hardware.