The child is allergic to cats, not dogs, so any dog will do for that.
Some people on this thread should stop thinking that they are the protectors of All Dogs from bad families. It's hilarious that I cannot expect to:
1- get a dog who will be part of the family but help teach a child in particular about responsibilities and long-term care and friendship. What happens when the child is not at home to feed the dog but dog feeding is her responsibility? The dog will go without dinner, of course! What if she asks to get a trainer so that she can learn how to communicate successfully with the dog? Hell no! You need to fail because a handful weirdos on mumsnet say so! Taking the dog to the vet with me? Nah, we need to prove to the weirdos above that we are totally irresponsible dog owners.
2- get a dog who will 'feel the love' my family can give and therefore like to snuggle up or pass time with my child/ren. What happens if the dog comes into the room while we watch a movie and wants to join in family time? We will kick him out in the garden because that's where dogs are supposed to stay!
3- get a dog that I can take on walks and play ball with. Got the message, first time my child wants to do so I will lecture her on why dogs are not bought for her fun and amusement and therefore she will never be allowed to do that!
I mean, I am almost 55, I have managed to raise children without getting them killed, I have fought very bad illnesses, I have psychologically survived very dear people's deaths, I have 4 degrees, managed to keep a job for decades, visited some really dodgy countries and came out alive, and even today, I can comfortably say I am not doing that bad, however yeah, a rescued or purchased dog will be my demise and will show how shit a human being I (and my entire family!!) is or will be.
To the other posters, who are telling me helpful information, thank you!