You have gotten a lot of good advice.
I also rock my daugter to sleep as I sing Silent Night. She's 19 months old now and has sung along with me for a long time how. Her voice goes up and down perfectly with all of the notes. I wouldn't change our cuddle time for anything in the world.
I handled my son in the same way, but he was a little more difficult. He would wake up like your little one, once the rocking stopped. The best I could do with him was get him used to a different rythm by patting him on the back.
I started patting him gently while rocking him and then carefully layed him down in bed (still patting him). Then, I'd lay next to him and continue rythmicly patting him lighter, and lighter, and lighter until I felt like he was in a deep enough sleep. Then, I'd slip away.
The great thing about getting him crossed over to the patting was that, if he cried, I would only have to come into his room and pat him on the back without taking him out of the crib/bed and sitting down to rock (kind of a disruption). He could go back to sleep in a matter of seconds with my touch.
But, I took months to transition him like this. There was a long stretch of time from initiation to freedom.
If this works for you, let me know. Wouldn't it be nice to just rub baby's back with a couple pats (just to let her know that you are there) and off to sleep she goes?