I can recommend an excellent private GP on Collins St - they don't bulk bill, though; long consultations are $80 and short ones $40, before rebate. They are fantastic though - they really know their stuff and are dedicated to finding out What's Up and helping you work with it.

Also re: pizza - Mr Natural's Vegetarian Pizza (on Brunswick just on the north side of Alexandra Pde) specialise in gluten- and dairy-free pizzas. Are you familiar with menulog.com.au? It is awesome, and probably the best way to find just what will deliver to you in the vicinity.