Output match is a 4:1 impedance transformer, so with a 50 ohm load, the collector impedace is 12.5 ohms, with a 12V supply, 4W seems on the edge of possible (3W is probably more realistic).
Note that 16dB is 100mW drive for 4W output, not 1mw (Would need 36dB gain)!
It is proably not hugely linear, being as the RF feedback at high frequency is falling off the side of a cliff, but for the stated application (A simple QRP rig) it should get the job done with the addition of a suitable output filter.
If they are available locally, something based on a RD06HVF1 mosfet will likely have more gain, and potentially better linearity, but whatever works.
Regards, Dan.