The Hayflick limit only applies to healthy individuals (and their tissues) with no change in activity of the telomerase enzyme. If the girl exhibits her appearance because of a telomerase mutation, she is not subject to the normal apoptosis condition.

Isn't it conceptually just like a counter which effectively turns off the cell copying after enough copies are being made? Before the limit is reached, the length of telomerase doesn't influence the quality of the copying. I don't see how it has anything to do with 8 year old looking as one year old. That has to do with gene expression, not with the limit of cell copies. But the limit of the cell copies will limit the length of her life, if I understand? And that's only one of probably many built-in expiration dates we have.

If something is wrong with her telomerase activity she will be extremely prone to carcinogenesis.

Remember that a cell has to accumulate many mutations in order to become cancerous. One of the most important aspects of cancer is that its cells are immortal. The cells of a normal person have to overcome this barrier in order to become cancerous so that, if her cells are indeed changed as you postulated, turning into cancer cells will be much easier for them.