Boost the signal of an FM transmitter using an “emitter follower” transistor
An emitter follower doesn't amplify the voltage of a signal, but it amplifier the current driving capability. For an FM transmitter with a small antenna (high impedance), what you really need is increased voltage, not increased current.

There are ways to match impedances between an emitter follower and an antenna, but they require many components and some tuning to get it correct. 

You would be better to use a common-emitter amplifier and you can reuse some of the bias circuits for Q1:
  Tie the base of Q2 to the base of Q1 via 10k, and add 27 pF between Q2's base and Q1's collector. Connect the emitter of Q2 to GND via R4 -- 47 ohm -- bypassed with 10 nF. This will run about 100 mA (same as Q1 -- seems very high for this application). Put an inductor (choke) or 27 ohm resistor between the collector and supply, and connect the antenna to Q2's collector.

Your biasing for Q1 seems high -- generally 470 ohm or even 4.7k should be OK for R1 (10 mA to 1 mA bias).