I saw this beauty while aboard Spoilsport with Mike Ball Dive Adventures in the Coral Sea, Australia in 2008. I was on the surface taking this photo and was surrounded by about four of them. They were very curious, approaching the ship to investigate divers.
From what I recall, Dwarf Minkes come down around July/August which is when I saw them, and they are really curious. They will approach boats and are tolerant of folks snorkeling with them.
These whales will even approach divers. In Oz the practice is to throw a rope out the back of the boat and everyone hangs on (meaning that the divers are not jumping in the water after the whales).
I remember holding on to the rope and the whales just coming out of the blue right at me. I was watching one of them that was about 6 feet directly under me (which of course meant my snorkel filled with water!) and once he left I turned around and there was another one, just heading straight for me. It was an amazing experience.