B.K.
No, it's not too soon.
When I started weaning my kiddos from the bottle I'd put the bottle away and give them a sippy cup when they were playing and at meal/nap times I'd offer both, the sippy cup and the bottle.
After a couple of weeks or when they seemed more into the sippy cup, which ever came first, I'd put the bottle away during meal/nap times, so they'd only have the sippy cup. If they just weren't having anything to do the cup I'd let them have the bottle for a few mins after meal times. I also just stoped laying them down w a bottle or cup if seemed fine. After a while they'd just get used to not having it.
My son had a harder time to stop w the sippy cup at bed time, so I just started putting water in it. After a few weeks the cup was still totally full in the mornings.
My daughter didn't take to sippy cups at first, but I found little cups w lids and straws at wal-mart, and she took to that. I'd offer both, the sippy cup and the one w the straw to her at meal times. When she was done and wanted to take her cup w her I'd give her the sippy cup, she would get mad becasue she wanted the one w the straw. I staied strong on that and about a week later she liked her sippy cup becasue she could take it with her to play.
For both of my kiddos if they were having a "bad sippy cup" day, it sometimes helped if I gave them the bottle, let them have a drink and then pour the rest of it in the cup. That just depended on their moods, sometimes it worked and other times it didn't.