All three are theoretically grammatical, but in the US none of them would be used. You'd say instead: "After I change his diapers, we'll do something."
1. After changing the diaper, we will do something. 2. After diaper changing, " . 3. After the diaper change, " 1. Why would you change "the" to "this"? What difference do you detect? I felt like it was something I'd say if I was closely involved in changing an actual diaper. eg If I had one in my hands.