DC to AC Inverter for WPT
Yes it's correct - due to air core "transformer" there is need high frequency to transmit power with good efficiency.
Check currently applicable standards: Qi and A4WP. 
Note that you need not only inverter - rectifier receiver too. As it was said the best option it's to use dedicated drivers. But educationally you can build your own driver too (it won't be easy).
Here examples of schematic from EPC9113 eval board: