I've seen pictures of anime and sometimes they belong to animes but the links never present names. Does anyone know of any anime in general though that has a female character obsessed with pandas or that's her quirk?
Nope. Maybe they wear a panda outfit for half an episode because it's a throw-away but nothing that's repetitive. If there is a panda obsessed person in the show, it's usually a male.
Like:
Genma Saotome from Ranma 1/2 turns into a panda.
China and Hong Kong from Axis Powers Hetalia are all up on panadas.
Pandaman from One Piece is exactly how his name sounds.
In Yakitate!! Japan, Mokoyama disguised himself as a panda for his second rematch with Azuma. He lost to Azuma, but he became a real panda (weird, I know).
There is Mei Chan from Fullmetal Alchemist has a pet midget panda which is frequently mistaken for an oddly-colored cat. But it's because she's from the FMA version of China.