If you mean in the same room as you, you can let baby to sleep on his own crib since newborns.
If you are referring to toddler bed (in the same room as you), you can switch after he/she turns 1 year old. However, it is recommended to use bed safety guards to prevent from falling down.
If you are intending to let your baby sleep in his/her own bed but in a separate room, this will depend on how ready is your child. For me, I prefer to stay close to my kids when they are young (below 3 years old) and save the troubles I need to travel between rooms at mid-night. My daugther transferred to her own room and bed happily after she turns 5 years old. For my second baby, he is more ready to sleep on his own bed and room at the age of 2.