There is a dog in the book, but nothing too bad happens to him. In a fight in the end of the book he bites someone and gets punched/kicked away, but there is no mention of him getting hurt.
Apart from the comment you can find under "Does a cat die?" I don't think there's any mistreatment of animals. Protagonist at first didn't like cats, but after being with them for a while he starts showing more affection. Camels are used for transportation, but there's no mention of them being abused.
Protagonist says that people in his country don't like cats, and that they would kill/abuse any that got close to them. This doesn't >happen< in the book, but the description made me uncomfortable.
The story takes place in a culture in which male polygamy is accepted, and men are described as having multiple wives. I don't think this applies as cheating, but is worth mentioning.
A baby "burps", I believe. I am not sure what this means exactly, because the only description is the word "BURP!" being 'said' by the baby and then his mother says she didn't know babies did that.
In chapter 4 the protagonist's family arrange for him to marry two girls who are described as fat and stupid, with ugly laughs etc. Not a "joke" but very negative connotation.