According to the OED this word is fewer than a hundred years old. Apparently.
Some people say okey-dokey and some say okey-doke. I suppose some say both (wishy-washy?) I say alrighty sometimes, and when I do it conjures up the way the bed-space air felt when we would bounce quarters before inspection, at camp. Alrighty has to do with the tautness of that flat blanket and the hope of a 10 and that space of time at the beginning of the day. (There's a bounce test for cranberries, too, but alrighty has little, if anything, to do with that. I have wondered for years about the floodings of the bogs on Nantucket, though . . . .)
March 21, 2010 addendum, okey-dokey sighting: Forty-five minutes into the play Red, Rothko tells his assistant, "Okey-dokey, let's prime the canvas."
Some might argue that okey-dokey is synonymous with hunky-dory, but they would probably be wrong.
February 23, 2018 addendum: The website of The American Scholar has an entire post dedicated to reduplicatives, of which okey-dokey is an example. My favorite bit: the sentence beginning "What is a dokey anyway . . . ?