Found: Sci fi novel: girl flees war with her dog, most of her village dies

The book starts out with a teenage girl living in a village near a desert. She's the daughter of somebody important, she has a fiance, she has a dog, her life is pretty good. Then her village hears that a war is coming and they're likely to get caught in the crossfire, so everybody packs up their stuff and gets ready to cross a desert to safety. The girl packs some sentimental items and her dog's favorite chewing rock (weird item, so I remember it!), but during the journey she loses just about everything she brings. A lot of the villagers die on this journey--some might get bombed by the people (aliens?) at war, some might die of thirst or starvation, some just get separated from the girl and she doesn't ever find out what happens to them.

Somewhere in the middle of the book the girl and one friend join another group of refugees, and I think they meet a man with a dog or jackal head who her friend ends up in a relationship with.

The girl meets a boy around her age at some point and they end up in a relationship and travel together.

I *think* that near the end of the book the girl ends up finding her mother or possibly both of her parents, and they have to travel through some kind of haunted cave in which her dog dies--I know something like this happens, but I'm *really* unclear on the details.

I read this book sometime between 2006 and 2018. Please help, I remember so many little weird bits and I want to read it again!

I found it! The Glass Mountains by Cynthia Kadohata