Does anybody know about my Barbie doll(1980s)?

I am trying to figure out a type of Barbie doll I have(it is my first Barbie doll as a child). She is from the late 1980s, probably 88 or 89, since I was born in 85. She is also a ballerina Barbie, she came with a light pink silky leotard, sparkly bright pink long tulle skirt with old fashioned type metal snaps. She came with shoes and a brush, and I'm not sure what else. She was one of the last dolls to have plastic non-bendable legs. She also has silky hair, not the soft kind.

I want to find out which doll she is so I can look for another one in better condition to put on display.

Does anyone know anything about this doll, or perhaps point me to a site with a list of all the Barbies ever made? Thanks!