It's that high because it's used as a penalty for people not registering their horses in a timely manner. I don't understand why she wasn't registered as a baby.
Do you know for certain that her parents were registered and DNA typed? Do you have certification from the mare owner stating that the foal was the result of a planned breeding by two registered parents?
You'll need all of that to get her registered.
It's also not $2,000, it's $1,000 after age 4, or $1,040 for non AQHA members.