Is a single FET a good way to drive a 100kHz signal through short coax?
With 100 kHz at 1 meter, your transmission line length is 1/3000 the vacuum wavelength of the signal. Maybe 1/2000 of the wavelength in the transmission line. Unless you have some really extreme requirements about signal fidelity, you don't even need to worry about transmission line terminations in this system. If you want maximum signal transmission, you can certainly eliminate either the source (R3) or load (R4) termination from this system. Most likely you can elminate both with no ill effects.

Second, your schematic shows the signal source has 2 V peak-peak AC signal on top of the 24 V DC offset. 

With this signal, I disagree with the two previous answers. You can arrange this so the FET will remain in saturation (the FET equivalent of "forward active mode" for BJTs) and your driver will have low output impedance throughout the signal's cycle. You won't see any meaningful asymmetry in the output. To do this you have to arrange things so the FET is always sourcing current into the rest of the circuit.

Currently you have maybe 13 mA bias current (conservatively assuming 4 V \$V_{gs}\$ for the 2n7002) through R1, and you're switching 10 mA signal into the transmission line, so your FET will remain saturated throughout the signal cycle. 

If you eliminate the source termination (R3) the signal current driven by the FET will increase, and you'll have to decrease the value of R1 to have enough bias current through the FET to keep it saturated.