I switched to Dvorak over a year ago. It took me a week before I could even attempt to touchtype at all, but my speed picked up rapidly after that. By the first month, my speed was faster than my old QWERTY speed.
I will warn you: learning to be able to switch back and forth required me to re-learn QWERTY. I instantly forgot my QWERTY training. However, I gained the ability to switch by forcing myself to do just that.
I find that if I take a glance at my hands (my physical keyboards are all QWERTY, although they are mapped Dvorak), I can force myself to start typing QWERTY. At that point, I can look back at the screen without reverting to Dvorak.
I don't actually know the Dvorak layout with my eyes or mind. It's more like my hands know it all by themselves. I can't picture the Dvorak layout in my head. I can't really describe the order of the keys. I can't even say what the Dvorak mapping of a QWERTY key is.
Typing became for me like walking. Without actually studying how one's feet move, it's difficult to create a believable animation of a walking human, but walking isn't a problem at all--it's just something we do.
Even though I can switch layouts, I'm still more comfortable in Dvorak. Sometimes I find it easier to take the fifteen seconds required to change the layout than it would be to continue on in QWERTY.