Is it a good idea to nurse my baby to sleep?

No. The key to infant sleep is teaching your baby to fall asleep on his or her own. Infants who fall asleep at the breast, or in your arms, have trouble staying asleep for long periods and often have overall poor sleep. I recommend a good, stable bedtime routine, similar bedtime ( sometime between 7 and 9), and putting the baby in his or her crib before they are totally asleep. Be consistent.
No. Very early on, your baby may nurse and then immediately fall asleep. This is really very normal. However, as your child gets older and becomes more alert, it is best for her to nurse and then be put to sleep while sleepy but in an awake state. This is to avoid sleep problems later on as some babies will require being nursed in order to go to sleep (a problem that is a bit more challenging to fix).