I did some design work on 125 kHz card readers. The transmitter and receiver coils are tuned to 125 kHz. I got about 10 cm range from a 10 cm coil, but the limit was getting the data back, not getting power to the card, but if you're getting the data back some other way you don't need to worry.
I also tried to get one to read with a single turn antenna of about 0.7m diameter. It didn't work, but there was enough power to activate the card at about 0.5 m range, and the problem was getting the data back from the card. I used a test coil to prove that the card was being activated. The current in the antenna was quite large, 8 A, if I remember correctly. I used a transformer to step up the current, and the tuning capacitors were on the low current side of the transformer, so the transformer turns ratio came into the tuning calculations. I used a ferrite ring as the transformer core.
Texas Instruments made a long range RFID system which could read a card at 1 m or so, but it used a different return frequency for the data. I think that it was 125 kHz one way and 132 kHz the other.
Keyless cars have a battery in the fob, and the 125 kHz is to trigger the key and to send data to it. The signal back to the car is at 433 MHz or something in that band, and is powered by the battery in the fob.