Everyone , including the dog, will have a great time, its not a third world country. Actually, I would be more concerned about the dog, having to go through quarantine. The issue with the child with health problems is that in an emergency, you will not want to trust an ambulance. Expats know to get yourself in a taxi, and get yourself to hospital. Or, get a driver that lives really close to you, so you can call him up. Other than that, the western doctors and medical facilities are excellent. Just make sure you have THE BEST medical package, eg Signa, Bupa with medi-vac. Maybe you could look for accommodation close to a 24 hour medical centre for peace of mind.
The schools are good, BISS and DULWICH both have the IB programme. Dulwich is in a nice family area with green spaces, villa’s , quiet wide roads for the kids to bike. There’s always lots of kids sports going on on Saturdays at the shopping/sports complex called Green City where there’s a Carrefour, Pines ( western grocery) Starbucks, etc. I don’t know anything about the area where BISS is situated, but my children went to BISS on the Puxi side, and got a first class education. Jinqiao is more of a suburb, but if you are putting your children first, then you won’t mind being further from the city anyway.
A lot of the housing complexes have excellent facilities, mine has an oudoor wave pool with a beach, two indoor 25m pools, two fully equipped gyms with free fitness classes, badminton/basketball hall, bowling alley, table tennis room, café. I look over an ‘English lawn’ where the kids have a kick around. And the dogs all meet up! lots of kids live here and get one of the many buses to the western schools. I could ask around if you want to know how long the bus journey takes.
If you want some contacts of other Aussies with kids, pm me.