I printed out a copy of the Dvorak keyboard layout and taped it above my keyboard. From what I recall, it took about a week to be even barely functional. I was already a very fast QWERTY typist, so it caused anguish to put up with such slow typing. On the occasion that someone needed something from me in a reasonable timeframe, I would switch back to QWERTY, finish the task, then go back to fumbling along in Dvorak. Never switch keyboard layouts in the middle of a project. :-)
I would say it took about a year to really reach my full Dvorak potential. Even so, over a decade later, I'm pretty sure that I'm still not as fast as I was on QWERTY. I just don't think you can match the muscle memory developed when you're young.
As for the RSI, I would say that you're better served by getting a high-quality keyboard that suits you than you are by switching keyboard layouts. Microsoft Natural keyboards are awful (sadly, I didn't know this when I was young and switched to one, which no doubt greatly exacerbated my pain). Get a keyboard with nice, light, consistent mechanical switches. An old IBM Model M will do, or a Das. My favorite is the Kinesis Classic, which takes an extra few weeks to adapt to, but IMO it's nearly ideal for programmers due to the excellent arrow key position (also, this help with Vim + Dvorak).