I think the diagram you show is quite primitive. The antenna will influence the transmitted frequency. It would be better to use a buffer transistor at the output of the oscillator (repeater on emitter maybe). I don't think you need to change from bipolar to FET. The TV spectrum is very large, from 48 MHz to over 800 MHz. What channel do you want to transmit on? For a short antenna, you should use higher frequencies. For lower frequencies, the antenna should be longer.