First, a 125 kHz square wave signal contains significant energy in higher harmonics, e.g. 1/3 the amplitude (a) of the fundamental frequency (f) at 3 times f, a/5 at 5*f, a/7 at 7*f... This means that the output coil is radiating at multiple frequencies, at least in to the AM broadcast band for a moderate quality waveform.
The wavelength of 125 kHz is (3 * 108 m/s) / (1.25 * 105 s-1), ~2,400 m (2.4 km). A quarter-wavelength is the "standard" moderately efficient antenna, so you could use 600 m long wires on the transmitter and receiver to increase range. That would be impractical for a classroom experiment, though.
You have some other ways to increase the range though:
- Use a parallel circuit tuned to the fundamental frequency, i.e. put the correct value capacitor across L1, calculated to resonate at 125 kHz on the basis of its inductance. Do the same for the transmitter output conductor.
- Experiment with odd harmonics, as above, i.e. tune both circuits to 375 kHz, 625 kHz, etc. This is a trade-off: reduced power at the higher harmonic is compensated somewhat by shorter antenna design.
- Experiment with a base-loaded 1/4 wave antenna. By inserting an inductor between the R1-L1-T1 junction and the antenna, the antenna/coil combination can be made to resonate at a much lower frequency.
You can combine a parallel-tuned "tank" circuit with a base loaded antenna and greatly increase range.