I'm 44 and an experienced accountant. I am bored and looking for a new challenge and I've seen an admin role offered at an institution (museum) which I've had a personal interest in for decades, am a current Friend of and would love to work for. However, it's nothing to do with accountancy- it's a general admin and fund-raising position. The pay is a lot less than I currently earn but I could afford the cut.
I've read through the essential criteria for the role and can make a good case for meeting them all (organisational and communications skills, professionalism, IT skills, relationship building etc.). They don't ask specifically for museum experience but they do want proof of an interest in the sector and knowledge of their work, which I have. However, I'm well aware that they probably have in mind someone much younger, perhaps looking for their second job in museum administration, and that's not me. I'm over-qualified, or perhaps better to say, oddly qualified for the role. I also have a completely unrelated doctorate- would it be better not to mention this if I apply? 
I wondered whether anyone had made a move like this? It's a very prestigious institution so I imagine they will have a lot of applicants. I don't mind having a crack and can take rejection but I'd rather not look a fool.