No, to drop off isn't used in the way you've used it in your question.
Consider this dictionary definition:
5 Set down or unload (a passenger or goods), especially on the way to
"he dropped the load off at a dealer's"
"his mum dropped him outside and drove off to work"
You can see from this definition's examples that off isn't strictly needed (although it is common to use it). You might drop your baby off at nursery, or at the baby's grandparents' house. It's probably best to avoid using just "dropped" with a baby, as it might sound like you literally dropped the baby.
I would interpret your two sentences as follows:
Your first sentence sounds like you were travelling somewhere, and on the way to that place you stopped on a baby chair to allow your baby to disembark.
Your second sentence sounds like you were travelling somewhere with a baby carrier, and you took your baby out of the carrier and then continued travelling (without the baby but still with the carrier).
You might instead use one of these sentences:
I put my baby in a baby chair.
I put my baby in his/her baby chair.
I sat my baby in a baby chair.
I sat my baby in his/her baby chair.
I took my baby out of a baby carrier.
I took my baby out of his/her baby carrier.
Or, for a sentence more specific to the situation you've given:
I moved my baby from his/her carrier to his/her chair.
I took my baby out of his/her carrier and put him/her in his/her chair.