I am not a psychologist by any means, but this is something I do have a very limited amount of knowledge on.
A fear of buttons is really not very uncommon. I actually have 2 friends with this fear. I have done personal research just because I am that way because I want to try to avoid upsetting them.
First of all the phobia is real and has a name. It is called Koumpounophobia. It is actually pretty common, but because it is actually an irrational fear the people whom are afflicted with it, feel like they are the only people in the world who suffer this way, but as I pointed out, I have 2 friends who have found they have the same issue, but different reactions.
One person dislikes therm so that they don't wear shirts with them, but they will "accept" pants/jeans, but that is it (and only one - no button up fly type). One friend gets physically ill at the sight of them.
It is important when raising any child (as it seems you are already well aware) to accept the child has feelings and allow them to express them, but teaching her it is nothing to permanently fear is important but will take time. Irrational phobias are never easy to deal with, as there isn't something easy to disprove. My two friends don't know when or why or how this started it's just "always been that way".
The research I have done says there are some helpful methods to work with overcoming this fear, but as I have not personally experienced it I don't have one to recommend. Best I can suggest is if it gets more aggressive consult a child psychologist. They may be able to help you determine the best course of action.
If it is just a phase or a "preference" at this point and you are able to pinpoint what it is (color, texture, size, shape, etc.) that's great and I wish you the best of luck, but if not, then, that would be my next suggestion.
However, bear in mind, and just FYI, Steve Jobs (of Apple Computers) also has Koumpounophobia and a very severe case of it, and if he can do what he has done - having this fear does not necessarily mean a guaranteed problem.