Yeah, I know about the Heels, but one can always hope!
Anyway, my only Doha experience was waiting there on the tarmac for hours when my plane was diverted from Dubai due to fog. They wouldn't even let us off the plane, so can't help there--sorry.
As for Phi Phi, there are a couple of very nice sites--Koh Bida Nok and Koh Bida Nai. These are also accessible from Phuket. Other than those two, the diving from Phi Phi is okay, but not outstanding. You might be able to get a trip down to the excellent Hin Daeng and Hin Muang to the south. Expect a loooonnng boat ride, though!
Where on Phuket is your friend's place? It might make a difference as to what you decide to do about diving. I mean that if it's up in the northern part of the island and you have to drive 40-60 minutes to get to the dive pier from there, you might decide instead to drive 90 minutes north to Khao Lak and do some daytrips to the Similans at least once.