What kind of doctor (gp, dermatologitst etc) would be best suited to diagnose and treat aquagenic pruritis?

Dermatologist. Although either doctor may be qualified, a dermatologist generally has more experience dealing with physical urticarias in their daily practice. They can also conduct further testing for other allergies (patch testing and prick testing) to determine if you are allergic to any other physical stimuli or substances.
Dermatologist. As with most medical problems there is more than one possible cause and effective treatment. Dermatologists can easily access all of the treatment modalities, but it is possible that they may need to try more than one approach to find out which one works best for you.
Trick Question. If you're already sure it's aquagenic pruritis, there's no need for someone to diagnose. If you have symptoms that are consistent with a textbook or internet description of the disease and just want a "second opinion, " both a primary care physician (family medicine or internal medicine in the us or gp elsewhere) and a dermatologist can diagnose and treat many skin conditions.