I think it depends greatly on the child tbh.
We got DC a puppy at five. We already had an elderly dog and DC wanted a dog to grow up with, so to speak.
We agreed on the basis that DC would have to do all of its care, and that to show he had the maturity and commitment for the next year he'd have to help me with everything our horses needed doing, 24/7, night and day, rain and shine. They had to come first regardless of what he'd rather do, without complaint and always with love, patience and care.
Sure enough DC did, and we got the puppy when the year was up (DC was 5 by then).
Several years on DC has been good as their word and done all of the care (with help where needed obviously) all the poop scooping, the walking, training, everything. They are the best of friends.
All of that said, I'm at home all the time and we have the space for DC to be able to walk and train DDog, and DC is unusually mature and selfless. Without those I wouldn't have entertained the idea. So in your case no, but not because of your DC.