"History of the DC Universe" did not include Batgirl on its retelling of the Post-Crisis continuity. It is not clear whether this omission was in error, or because just like in Supergirl's case, Batgirl as a character was going to be removed from the new universe.
However, when DC published an update of Who's Who in 1987, Batgirl was officially reintroduced. For the most part, most of her history remained unchanged; for instance, Barbara was still a librarian and former Congresswoman, she retained her photographic memory, and her debut happened on the night of the masquerade ball when Killer Moth tried to kidnap Bruce Wayne. Despite this, other substantial changes were made, compared to her original Who's Who entry.
Batgirl by Rick Leonardi
Barbara was no longer the biological daughter of Commissioner Jim Gordon, but his niece and later adopted daughter -I don't understand the need for this change.-
In this new reality, Barbara had always wanted to be Batman's partner, whereas in the Pre-Crisis Earth-1, it was Superman who had inspired her to become a super hero. In recent years, this was changed once again, and the original Black Canary would become her new role model.
The biggest change for the character -in order to explain her absence after the Crisis to the time of this update- was the fact that she had practically retired from the super hero life due to her sense of failure during the Crisis. One year later she finally gave up the cape and cowl, and one year after that DC put the final nail on the coffin of the greatest version of Batgirl during the events of "The Killing Joke".