i think the best time to start underwater photography is when diving is second nature to you. you don't worry about buoyancy (which also implies you do not kill stuff with your fins, use pointers as walking sticks, and grab on to anything to stabilize yourself), you have good situational awareness, and am fairly confident in diving.
i've seen many divers with terrible situational awareness struggling to take a picture of something, and kicking up all sorts of sand and silt, and breaking coral in the process. now, everyone will say "not me! i'm a responsible diver!" but you wont know until someone tells you off, or you ask the people in your dive group.
also, when you dive with underwater photography in mind, you tend to have a different style of diving. it's no longer a tour around the reef like before, but more like 15 minutes at a rock, 10 minutes at a seafan, and before you know it, everyone else is gone and you're all alone.
basically, if you can't dive well, you won't take good pictures.