P.A.
If you have dropped the mattress of the crib as low as it goes, then, I see no reason not to begin the transition to the bed. In our family, we've had a variety of sleeping issues; climbers, thrashers, claustrophobics and night terrors.
the other posts offer good suggestions regarding room saftey so I won't repaet that. One child was so athletic and thrashed so much at night, we placed her on her crib mattress directly on the floor. it worked so we well, we never purchased a toddler bed. When she was ready (about age 5) we went strait to a big girl bed (a low one mind you).
FYI: oldest girl - toddler bed - 15 months (prep for new baby)
God daughter - mattress on floor - 12 months
Middle son - toddler bed 18 months (tiny but a climber)
Nephew - toddler bed 12 months (claustrophobic)
Youngest girl - toddler bunk bed (lower bunk) 15 months (went by herself for a nap one day - I think tired of being separated from siblings - caused middle son to move to top bunk at age 4.5 - scary but all worked out great)