Poverty, Neglect, and Abuse are three different things.

Since you seem to state (At the end of the logline) that the child’s goal is to escape the abuse, then at the beginning of the logline you should give us a direct example of his abuse.

However, I would add, that a logline for a story like this is quite a bit harder to write.
Because a big part of the story is about something going on inside the kid’s imagination (Sort of like, the secret life of Walter Mitty)
On the other hand, there seems to be an outside of the imagination story as well.

This makes the logline more difficult if half your story is an imaginary story inside the child’s head and half the story takes place outside.

This is the kind of story I like, but the logline will be a little more difficult.