If it's any consolation I've just bought the 6x3x3 happyhutch too and I'm really pleased with it, I don't think it needs reinforcing, the bigger ones are made with thicker wood etc anyway and I don't see how the mesh could be any smaller! The only addition I have made is some bolts for the doors and hasp/staple type catches for the run lid to make sure that a fox can't open the swivel catches, and I will do some weather proofing for the mesh parts for the rain. It arrived really quickly too, even though the site says they are made to order. I have put Lino down on the floor to make it easier to clean (do it before you constuct the hutch so you don't need to cut around the joins!) and have put sealant around the joints on the inside, and now I'm in the process of ripping out the old playhouse and run and getting the ground ready to put the new one in while the newlyweds are bonding.
Good luck with yours, I hope you're as happy with it as I am with mine!