You are unlikely to get apples like Pink Lady from your seedling. Even if self pollinated the fruit won't be the same as the parent. But it would be interesting to see what kind of fruit you do get.

If you have the apple tree, just take a cutting in early spring.
That is before the buds open.

Karyl

Seeds are produced via plant sex. The seeds from that apple certainly have Pink Lady for a mother, but some unknown variety for a father. Often times it is an inedible crab apple that does much of the pollination for the big orchards. So the resulting fruit will most likely be nothing like Pink Lady, just like a human child is different from its mother. There might be some vague similarities, but... probably very different.

Dear dmtaylor,

A very serious thank you for your comment. I know it was five years ago now, but i have been scouring the internet for information about growing apples from seed because I am in the process of attempting it now myself. ( I am going into the task fully aware that the apples my little seedlings eventually produce ( if any ) will be vastly different and probably less palatable than commercially grown varieties ) You have managed to sum up everything that the internet has taught me in one concise, easy to understand paragraph.