I believe that /P is a valid field 10 code for carriage of a Mode S transponder, including pressure-altitude transmission, but no aircraft identification transmission. I don't think /Q is defined in PANS-ATM, but I notice that it is a valid field 10 code in an FAA flight plan for RNP capability with RVSM.
Would the codes you have seen happen to relate to a flight plan filed to/from the US as this may explain the /Q?
Cheers, NavMonkey.