I tested my transmitter with a new 9V alkaline battery and it went far. After about 1 hour the voltage was about 8V and the range was less.
It should have more power output with an 11V supply but I don't know how much. The output transistor might be OK or might get too hot and melt.
The drive level to the output transistor is fixed so there is a minimum supply voltage where increasing it won't increase the power output.
The 2N3904 is a general purpose audio transitor, therefore its gain at 100MHz is a max of only about 3. A real RF transistor would have much more gain, give a much higher output power, require an emitter resistor to limit the power and require a heatsink.