Hee hee. Welcome to the World of Poo!
Seriously, these guys poop a lot. I think they poop on average about every 10-20 minutes. However, it can be more frequent if:
-They have just eaten
-They are excited (i.e. I've just been let out of my cage!)
-They are frightened
-They are in a new or unusual circumstance
-Many other reasons
Every weekday morning Horatio sits on his little stand on the table and eats porridge out of my bowl as I'm having breakfast. As soon as the bowl is empty and I pick him up, he poops. Well, after several "accidents", I now know to hold him away from me until the deed is done, then I only have the floor to clean (not myself!).
It sounds as if your little monster is pretty "regular" when he comes out of his cage, so just hold him away from you (or over a suitable area) until he poops. Some people have been able to partially toilet train their QP's, but I think it's the exception rather than the rule. Most of us just buy a lot of wipers.