i belong to a menopause forum and you'd really be surprised at how old some ladies are who still get regular periods - up to 60! i think the danger sign is if your periods have stopped for maybe a couple of years and then start again, definately needs looking into. but it's my guess that you're actually only on the old-ish side of normal for still having periods so i do wonder if your doctor would do what you're asking if there's no medical reason.
but, to answer your question, yes, of course you're entitled to ask if you can have it done, although whether it would bring the peace you're after is another question! sometimes, it's only after the periods have finished that the 'fun' really starts in terms of symptoms, and lots of ladies wish their periods back!!
good luck with whatever you do though - been there, lived through it, came out the other side still in one piece :)