Learning Old English is, well, actually sorta limiting if you're using that as your primary focus. Something broader -- Old English, along with studies of the medieval era in general, some history-- could turn into lots of interesting stuff. Not particularly lucrative, but if you enjoy your job, and don't act stupid with your money, who cares?
People have already pointed out a few uses for that knowledge. If you combine it with something very different, you can get even more possibilities... heck, Tolkien wasn't exactly a low-profile guy and he turned his knowledge of Anglo-Saxon, Old Norse, etc into Lord of the Rings, Silmarillion, Children of Hurin, etc. Or whoever the guy was in Monty Python... I forget the name.. who wrote the script for the Holy Grail. That guy's actually well-known amongst the medievalist circles as a respectable scholar! There's reputedly a ton of obscure jokes hidden away in there that only medievalists get. There's even some music artist (I forget who), relatively well-known who bases alot of his material off medieval poetry, and even sings some of it in wahtever language. Oh, yeah. And there's Benjamin Bagby, who tours the country, singing Beowulf in Old English for audiences accompanied by an Anglo-Saxon harp(which he plays). Apparently is doing quite well off it, as well as having one heckuva job! Even has a DVD out.
And Wagner. Not exactly the greatest role-model, but still... His medieval-legend operas made him more than a little famous.
Anyway, enough with annoying you with my little tirade. Bottom line, I would suggest learn it, but make sure to keep a broad field of study anyways (something people keep telling me to do....)
It's great fun (I'm just starting to teach myself Old English in my senior year of high school with a teach-yourself curriculum I bought for waaaay too much money.)
You might be interested in this guy's blog, too. He's a medievalist professor. Might give you some idea what it's be like to base your life around medieval studies
http://unlocked-wordhoard.blogspot.com/
Good luck, whatever you decide!