What about tuition? I think you have more than $1181 in QEE, unless you go to a school that charges $1000 in tuition and $20k in room and board.
If you have $10k in tuition, and $1181 in other expenses like fees and books, you have $11181 in QEE. Subtract your $4202 in scholarships, and you still have almost $6k in QEE so your parents can take the full AOTC.