No, your derivation is not correct.
You cannot multiply the voltage strength by the distance to obtain a voltage. Furthermore the "power" you have to calculate is not referred to the 50 ohm.
In case of a isotropic radiator (that is the power is equally distribuite over the surface of a sphere), from the EIRP we can calculate the Pointyng vector magnitude:
P = EIRP/(4*pi*d^2)
then we know that in far field P=Zo*H^2
where Zo = 377 ohm, H is the magnetic field in A/m
thus:
EIRP/(4*pi*d^2) = Zo*H^2 from which:
EIRP=(4*pi*d^2)*Zo*H^2
numerically:
EIRP = (4*pi*10^2)*377*(126e-6)^2 = 0.0075 W or 8.76 dBm
However this is an RMS value, the quasi-peak measurement requires a correction that depends from the waveform