I don't think having breakfast at your desk is a problem (unless it's kippers), but if I didn't want to be interrupted, I would go away from my desk. I occasionally have a bacon roll at my desk but I'm usually checking email while doing it. (I did discover last week that holding a half-eaten Magnum seriously impedes my typing speed, though.)
That doesn't mean it's okay to interrupt me just because I'm at my desk - a colleague tried to ask me a question the other day when I was on the phone. When I turned and gestured at my headphones, he tried again, instead of saying, "oops, sorry, when you're free..." as most people would. It turned out not to anything important - if we'd had a priority 1 outage just come through, an interruption would be expected. Other times, I will say things like, "I need to finish this first, then I can think about it," or, do you need an answer now, or can it wait till after the meeting/this afternoon/tomorrow /next week?" I usually can move things around, but sometimes we need to negotiate, as our priorities don't always match. I try not to be too rude, though. I think there have been times when I have failed, but usually not.
I think there are a number of things I would look at.
Other than team feeling, does it have an impact on productivity? I'm not saying that an sense of team isn't important, because it definitely is, but if there are any more tangible things, like deadlines being missed, data missing from reports, procedural errors - that can make a more measurable problem.
She doesn't take well to negative feedback - can you frame it in a more positive way, more constructively? I think she should be made aware of the discord she is causing -maybe she will have other ideas on how to resolve it, without pissing people off further. Maybe the issue is her colleagues' perception, but it's not beyond her powers to change things to improve their perception. (It sounds like it's not just their perception, but she may see it that way.)
Do people really need to ask her questions at that time? Some things are urgent, but others can wait. Sometimes, asking other colleagues is a shortcut, because it's quicker than looking through documentation or working it out for yourself. We all do that sometimes, and there are also aspects of social interaction and bouncing ideas off others, but that doesn't mean it's essential, especially not with that person at that particular time.
I agree that no one should be indispensable - but I also know that even if everything someone knows is documented, so others can pick it up, there will always be some people who are more thorough in their work, better at seeing links across
different areas of work, better at remembering that something is like a problem that happened last November, better at finding information...