Honey...do it NOW!!! I know you have lots of answers, but here's my two-cents! My son was moved to a toddler bed when he was 13 months old, not because he was climbing out or anything, but because we are expecting #2 and wanted him out of his crib for long enough time to feel comfortable with the baby sleeping in "his" crib. My son is also very small, but he does fine. The only reason we didn't get a twin bed with a rail is due to space in the nursery, but the toddler bed is wonderful as he can climb out and in himself and your daughter might love a princess or Dora bed. He did fall out a few times in the middle of the night, but he was fine...didn't even wake up most of the time and the times he did, it was easy to put him back into bed! I wouldn't be afraid to transition her...these kids are really more resiliant than we give them credit for!
We bought a travel-size pillow and put it under the fitted sheet, which he loves and the comforter and sheets don't go all the way up to the top, so I don't worry about him getting buried. As far as safety, we put a tall gate at his door and childproofed all this room, put a few safe toys and books in his room so when he gets up in the morning, he can play a little before waking us up- though this rarely happens now since he is potty trained so within minutes of waking up he's at the gate asking to go pee. Granted, I often walk in to all the toys and books off the shelf AND the drawers emptied of clothes as he often plays a bit before bed. I also would put a spill-proof glass with some water (may help with the bottle transition too, but he no longer has this as I don't want him wetting his bed in the night) and a few "love-ies" in bed with him...even bought him a glo-worm that sings and lights up that he loves to push as he goes to sleep.
At bedtime, we put him in bed and then if we hear him get out, we put him straight back in and tell him good night. At the stary sometimes it took 5-7 times of putting him back before he goes to sleep, but other nights we put him in once and he goes right to sleep. As he got used to sleeping in his bed, we did occasionally find him asleep by the gate and I would just lift him into his bed and everything was fine. He did go through a stage of about a week where he didn't want to fall asleep in his bed, so I picked my battles and we bought him a play tent and told him he had to pick one or the other...he loved sleeping in his tent, but now it is old news and he is back to sleeping in his bed! If you are concerned, do a few days of a trial run during nap times. Anyway, good luck with transitioning. It is well worth it!
Oh, BTW, I have a post in that I asked a similar question, so you might check that out in my profile too! Good luck!
S., 26, mom of 18-month-old and #2 boy due in Aug