Great question! I've been on both sides of this dilemma.
Having caponized birds before, I will say that it's something that needs to be thought over thoroughly, and not taken lightly. Dogs and cats can be put under for surgery a lot easier than birds can. I had About 1/3 of the capons die after the process. I no longer caponize, as it turns my stomach. But I have nothing against those who choose to.
Bird anatomy is also different than mammal anatomy. The testes are located well inside the body in birds. You have to make an incision at the right place in a bird's side, and use some scary Frankenstein looking tools to spread the rib cage apart and to locate and remove the testes in a rooster. They bleed, it's kinda freaky to be totally frank. I am sure that spaying female animals is similarly scary but again, dogs and cats respond better to anesthetics.
With that said, your daughter's rooster does look just about the right size for the procedure. Just be informed about your decision, whatever it may be.