I had to laugh when I saw this, because I just went through this with my daughter on Sunday!
I had the same questions. When I asked my pediatrician, she said that it's advised to move them into a toddler bed at 18 months, or when your child starts to show signs that he/she can climb out of the crib. She also said that the reason you want to move them when they can climb out of the crib is because if they try to get out when they are sleepy, they can hurt themselves. If they can actually get out completely, your time is up no matter how old they are. By the way, my daughter is 24 months, but I didn't ask this question until her 2 year appointment because she just started climbing out of the crib. We didn't know we had passed the recommended time table! Our time was up so we had to move fast!
As for moving around and not sleeping, when I searched the web for what other mothers had experienced, some said that their child moved around in the dark a lot on the first night, then less and less as the room became less of a "wonderland". One mother left a nightlight on so her child wouldn't hurt himself while exploring.
Here's what I did:
First I did an extra thorough check for child safety, like tethering dressers to the wall and such, sliding outlet covers, etc. (they sell great outlet covers at onestepahead.com) Then I had my daughter help with the transition. Since I have a convertible crib, she helped with changing the bed from a crib to a "big girl bed". She helped loosen the screws and remove the front rail, etc. Then she did jump on it a bit because she was so excited. But then, when it's been time for bed, I read to my daughter, and sing to her in the dark, our normal bedtime routine, until she gets REALLY sleepy before I would put her down. On the first night, by the time I put her in the bed, she was so tired, she didn't feel like exploring I suppose! It's only been a week, but so far she's only gotten out of her bed once to get a book! Otherwise, she's stayed there! I also chose not to use our nightlight, because she doesn't normally use one, and I didn't want her to suddenly become aware of all the things she can see in her room at night. I hope some of that helped! Good luck!