What kind of book? I'm a published author (decidedly non-famous!), but might still be able to guide you a bit. My first thought is that a kids book would be the best entry point if you want a beardie as a main character as they're cute & lovable, and do things kids would find entertaining. If that's not your bag, you could write one in as a companion animal.
The concept of a 'familiar', a creature companion that enhances the powers of a magician, is known in the fantasy genre (my book's genre), so that's an avenue. I think in order to make a beardie the central focus of a book otherwise, you'd need to give them more human-like attributes. That is do-able but not necessarily easy because too much & people would no longer be able to relate to them as beardies, and too little & your story arc is limited to their behaviors and traits for the most part.
A young adult novel about a person's struggles and their bond with their beardie (and how that has affected them) could be either fiction or non-fiction depending on your personal experiences, too. You might tease these & other ideas out in a short story to start, to see if whatever you choose has enough 'legs' for something longer. I found a few of my early ideas wouldn't work over the length of a novel, and so kept bits from those efforts in what ended up being the finished product. Hope this gets you on your way!