The furry fandom, explained plainly

The furry fandom is a community built around anthropomorphic animal characters: animals that walk, talk and think like people. Its public image and its reality are far apart.

It is mostly art

Most fans invent a character, a fursona, and commission artists to draw it. Commissions support a working economy of independent illustrators, writers and makers.

Fursuits are the famous part, and the uncommon one. Survey work by the International Anthropomorphic Research Project has consistently found that most fans do not own a full suit.

Conventions

Conventions such as Anthrocon in Pittsburgh draw thousands of attendees and raise money for charities, often animal shelters.

Why the name works beyond the fandom

Furry plus quest reads naturally as a children's adventure game, a pet brand, or a mascot-led product. Short, spellable and cheerful.

What you could build here

Three directions that would work on this name. None of them is the only answer — it is your name once it is yours.

1. A game. The name already sounds like one: an adventure with animal heroes, for any age.
2. A fandom hub. Art, characters, conventions and commissions in one place.
3. A pet brand. Read it literally: adventures with your dog or cat.

What it could look like

A sample concept, built to show the name in use. It is a starting point, not a business that exists.