At 300mW you won't need any further amplification to measure the frequency.
What is the input impedance of your frequency counter? It's probably a safe bet - and especially given its low working frequency - to assume it's high (...perhaps of order ~1Mohm?) The most important thing to be done for the measurement is to make sure the transmitter is correctly terminated into it's nominal output impedance, which is generally 50 ohms.
If your frequency counter input impedance is 50 ohms, you can directly connect the transmitter to its input - but beware it's maximum input power/amplitude/level specification. 300mW (which equates to nearly 25 dBm) is a respectable level - and this power will have to be dissipated by the termination within the frequency counter. It might be OK, but check on your counter design - this power is beyond the ratings of the 1/4W carbon resistors of old and small SMD resistors. If the counter can't handle the input power, you'll need an inline attenuator.
If the counter input is Hi-Z (high impedance), use a (BNC?) T-piece: connect the transmitter to one port, the counter to the other and a 50 ohm terminator (rated at > 0.5W) to the last. To avoid transmission line issues, the T-piece & terminator should be located right at the frequency counter input with no interconnecting coax. You can use an arbitrary length of coaxial cable from the transmitter.
300mW equates to sqrt(P*R) = sqrt(0.3 * 50) = 3.9 Vrms (~11 Vpp) in a 50 ohm load, so your counter will have no trouble accurately measuring the signal. Make sure the modulation of the transmitter is turned off (i.e. so you're only transmitting a sinusoidal carrier) so that the (otherwise broad) output spectrum doesn't corrupt your frequency measurement.