I don't know for Dvorak, but it took me one week to become sufficenty proficient in Colemak layout.
I don't want to start flame wars, but since you are coder you can give it a try since it is better suited for code. Interpunction is in the same places as in qwerty, and some basic shortcuts including letters z x c v q w a are in the same place as in qwerty.
Regular typing took me a few weeks. Programming took MUCH longer because braces, parens, etc. are all somewhere else -- and my hands are hard wired to do shift-[ and shift-9. You can always re-map them, though, which is what I ended up doing (same with ctrl-c, ctrl-v).
I would definitely recommend remapping the common keystrokes, otherwise you'll be an absolute useless person if you ever temporarily use another person's computer :D
this is an interesting question, but could you clarify something? are you asking because you've committed to learning dvorak to increase your general typing proficiency/efficiency, or because you want to improve your coding proficiency/efficiency? i dont see how mastering the dvorak keyboard layout makes one a more efficienty/speedier coder, as the layout wasn't designed with that goal in mind.
I use (one of the many) Spanish Dvorak layout and I got used to it in about a week. Getting my speed back took a little longer; it depends on how long it takes your brain to adapt to a second layout and how much you type with it.
Be aware though, some people have troubles switching back and forth to qwerty and you might be unable to use dvorak in some computers (In my case, I had to create a custom keymap and install it)
Learning to touch-type on Dvorak doesn't take long. Print out a Dvorak layout and stick it to the bottom of your monitor, and just look at that when you're not sure where a key is. You'll be typing in comfort within a few days. Coding won't be comfortable for about another two weeks.
I personally find the Dvorak keyboard layout much more comfortable than QWERTY... but it is important not to forget QWERTY as you learn Dvorak. I learned Dvorak back in college, and once I went to an interview where they tested my typing skills... and they brought out a manual typewriter! Oops! I had brought a floppy disk with drivers for Windows and Mac, but the manual typewriter was something I didn't anticipate. I spent some time on regular QWERTY every so often after that just to make sure I could do both.
One oddity with Dvorak... it puts the n, t, and s keys all under the least coordinated fingers on my right hand. When I'm typing a word that ends with some combination of n, t, and s I'll transpose the letters a bit... but only when I'm typing at full speed.
So I'd encourage everyone to learn Dvorak, especially if you plan on typing for a good chunk of your professional life.
Took me about 12 weeks of programming to get used to it and been using it for years. Have to look at the keyboard to type use Qwerty. The two biggest frustrations are that coding punctuation is awkard to get to as has been noted and that CTRL-V (Paste) and CTRL-W (Close Window) are so close together.
When I switched over, it took me 3 days to get the layout down, about a week and a half to pick up significant speed at it. It took a couple months before I could type as fast (or better) than the QWERTY layout doing code.