Seeing as how 90% of the frum crowd lives in a metro area, its really kind of selfish to have a dog, if you’re going to keep it locked up indoors most of the day. Add to that, by the time the child in question is old enough to take care of said dog, they are likely coming home after 6:00, so when would they walk it? Then its off to camp for 2 months, so that would mean its suddenly MY dog. Then there’s dog related issues on Shabbos that is very problematic, so that’s out too.
As for learning things like responsibility, loyalty, healthy fun, ect; that’s what siblings and friends (and ultimately spouses) are for.