This is probably going to flip you out, but Galadriel is much older than that!
According to the
Encyclopedia of Arda
She was born during the Years of the Trees. When the Elves awoke at Cuiviénen, Melkor was chained. This period was 2900 years. She was probably born within 900 years of that time. This would make her at least 2000 years old when the trees were killed.
Then came the 1st Age, which last 583 years. It ended with the War of the Wrath and the Distuction (sinking) of Beleriand.
The 2nd Age lasted 3441 years and ended with the Last Alliance. Then the 3rd Age, which was 3021 and ended when the Elves sailed to Valinor.
This would make Galadriel around 9000 years old