As long as the child is under 18 or still in high school (if older than 18) AND unmarried; they can get benefits. The child is entitled to 50% of the parent's disability benefit.
From what I understand, when you apply for the child at the SS office, you need to show proof of the parent's disability. I think your approval letter would be sufficient.
You can go to the Social Security's website for details:
Benefits For Children