Welcome to the board!
SuziSew and ckowl's calculations are correct. I would be inclined to make the quilt smaller than the dimensions you found, though; most college dorm beds are against a wall, so you don't need a big overhang on both sides (if the quilt is too wide, it's hard to make the bed). A long drape is also awkward if you're using the under-bed area for storage (a bedskirt is better if you want to hide stuff). I went to college with a quilt about this size, and it was just too wide to be convenient.
A twin XL mattress is 39 x 80". Dorm mattresses are usually 6-8" thick, so an overhang of 12" on each side is usually sufficient. This makes your quilt 63x92", which would require 25 x 37 = 925 squares. You could even make it a row or two smaller in each direction, without any harm.
As other people have said, this will be a very heavy quilt. There's nothing wrong with this, as long as your daughter knows what she's getting. If you want it lighter and haven't cut your squares yet, I would cut them bigger than you're planning, so that you have less weight in the seam allowances. Also consider adding sashing or alternate blocks of other fabric to reduce the overall weight.
Good luck with your project!