I was a thumb sucker too, and I have to say that with most kids who are thumb suckers there is an emotional connection attached to it.It brings them comfort and safety when they do it.
Your daughter may not understand why she is sucking her thumb, but maybe if you addressed some emotional issues in her life or things that have happened in her life it may make the separation from her thumb sucking a bit easier.
My emotional component of thumb sucking came from my parents divorce when I was about 2.
Her thumb and her sucking are also things that she can control- she can control when she wants to do it and doesn't have to rely on anyone else for that comfort. Forcing her to stop doing it before she ready might cause more problems. And as many have already mentioned- their parents tried all sorts of things to get them to stop, but it wasn't until they wanted to stop that they actually did.
I suggest sitting down with your daughter during a quite time and have an un-rushed conversation about why she sucks her thumb. Ask her why she does it, how does she feel when she does it, when does she feel like doing it: ie: when she's sad, mad, bored, etc.
And then mention that you are concerned about her sucking her thumb because of the the tooth issues that could happen because of it and ask her is there is anything you guys can do together to help create that feeling of comfort and security when she's feeling sad or mad to help replace the thumb sucking.
To take care of the boredom issue of thumb sucking teach her how to knit or crochet or something that keeps her hands busy and her mind active. Reading might not work because a free thumb can always go in the mouth while the other hand holds the book.
A six year old is not to young to learn to knit/crochet or think constructively about problem solving. The more you make it her thing and not something she does that annoys you, the more likely she is to be successful at stopping when she wants, and that most likely will be sooner than later if she's supported in the process.
The main goal is to be supportive of her feelings, allow her to make the decision to stop, and help provide activities that replace or distract from the thumb sucking.
Good luck,
M.