did you pick this chunk of spectrum at random? if so, why? the piece of spectrum you have chosen includes maritime and point-to-point communications. RFID is an ISM (industrial, scientific, and medical) application and belongs in the ISM bands. ISM devices are generally limited to 100 milliwatts, so your amplifier isn't legal even inside the ISM bands. the nearest ISM band is 6.765 to 6.795, and the next ISM band is 13.533-13.567Mhz. there are limits to the effective radiated power in those bands. if you operate outside the ISM bands without a license, you could get in a lot of trouble (how bad that trouble could be depends a lot on how your country enforces the law). if you operate within the ISM bands with your amplifier, you could get in a lot of trouble. i recommend you do one or both of the following: A) get an amateur radio license. you can operate (within the amateur radio bands of course) with up to 2000 watts. the 40 meter band (7.0-7.3Mhz) is very close to what you have put together. B) use one of the ISM bands i mentioned above, and keep your emissions below 100 milliwatts. the actual way those emissions is often measured is by how many microvolts per meter are picked up on a calibrated receiver. there are ways you could use your 15 watt amplifier, as long as what's radiated is below the maximum field strength (and that field strength usually works out to be the same field strength you would get running 100 milliwatts into a dipole antenna).
to answer your question about impedance matching, use an antenna tuner. i would think your amplifier is already a 50 ohm output, as that's what most radio equipment is designed for.