What is your field requirement in A/m at __ distance? The antenna usually means a coil around a big piece of ferrite. Therefore, it is narrow band if you can't afford too many losses. What is your input power requirement? If efficiency is important, then you may have a problem: The antenna is an R-L-C where R is small and Q is high. Look at the variability of the inductance and resonant frequency. Also saturation of the inductor will change the frequency. You will find it is the antenna setting the frequency requirement and not the crystal.
I would recommend either a free-running power oscillator at the R-L-C frequency or phase locking it to a crystal. Be careful when selecting the capacitor that resonates with the coil - the AC voltage can be hundreds of volts, depending upon your power output.
Kaschke makes some antennas of varying power handling for these 125 kHz applications. Some have the capacitor built-in and they are pre- tuned.
Frank