Bunny ears tend to go back to "the bunny eared lawyer" trope.
Although there is a long, long list of symbolism regarding the rabbit.
In the east, Kaguya-Hime is often associated with the rabbit because of the Taoist legend of The Lunar Rabbit. Search engines are your friend, here. "The tale of the bamboo cutter" and "the lunar rabbit china" will get you the related stories. As such, people associated with rabbits from the east tend to have white hair and be symbolic of the moon.
In the west, the rabbit is a little more associated with the concept of Eostre - which is the Vernal Equinox, or spring. Hence why we have the Easter (Eostre) Bunny in the Spring to celebrate the resurrection of Jesus. More than a few holidays were consolidated.
Because of this, a rabbit can often represent a state of relative innocence, of new life, or fertility/birth/rebirth.
Many people on the internet, and particularly among the anime-influenced, will blend the themes and symbolism. Without knowing much about this particular person, it is hard to say why they are using bunny ears. It could just be a play off of the pop culture, or it could have a deeper meaning.
For my works, I am using more eastern symbolism as those under the rabbit are related to Kaguya and the story of the chinese zodiac. You could project the broad western symbolism onto it and it work, so I don't try to write in isolation of it, but I make no specific efforts to express that symbolism.