Hi M.,
My son didn't get moved to a toddler bed until he was 32 months old. We were pretty lucky, he never tried to climb out and we were in no hurry to go back to the sleepless nights trying to keep him in his room. We used to use the crib for his time outs when he was really bad and one time when he was two years old he threw a bad temper tantrum and almost fell out and he never tried it since.
He kind of grew out of the crib so we made a big production of picking out a toddler bed and used the crib mattress in there and STUCK to his bedtime. We had a baby gate up at his door to ensure he stayed in his room at night (I heard horror stories of kids breaking out of their houses and wandering the street. Didn't want that to happen). But he was so happy to be in the new bed that we had no problem at all transitioning. In fact, he slept even better. We kept the crib up for 2 weeks as a deterrent to wandering the house because if he wandered, he had to go back in the crib. After one time of wandering and being put back in the crib, he never wandered again.
It is pretty much up to you and your daughter though, there really is no good age to transition, she will just give you signs. I wouldn't transition just because of the carpet though, but that is just my 2 cents worth.
I'm sure whatever you decide will work out fine as long as you have a plan and stick to it.
Sorry I was long winded. GOOD LUCK!