You can include the word her, or not. It doesn't make much difference. You do need commas after the words asleep, hole, and awakening, and remove the article the in front of Wonderland. Finally, you should move the comma after the word girl to follow the word who.
He told them about a small girl who, having fallen asleep, disappeared from the rabbit hole, and on her awakening, found herself in Wonderland.
Student or Learner