Probably. I was raised outside of the church so my understanding was that (infant) baptism is a way of welcoming the child into the church & the community, assisting in the passage to heaven, and presenting a couple of individuals (godparents, guardians) who would look after the child in the event of the death of the parents and also to provide guidance to the child during their lifetime. You can read 'guidance' as spiritual guidance if you are so inclined.
The Procession of Faith is specific to some Christian denominations. In my case, the choice I made later in life would not be considered a Profession of Faith as I profess to have no faith.
All these ceremonies have more to do with the mechanics of the church/religion than God. In my head I see the church and God separetly. If my child decides to believe in God and/or religion shes welcome to and I believe that if she does choose a God that he/she/they will not hold it against her that she didnt worship him/her/them for the first 14 years or so of her life. Maybe Im naive, I just dont think Gods are meant to be nasty.
I dont want her to be like my husband who was raised Catholic and resents it. Hes forever saying that he was baptised Catholic but hes an athiest. (and there aint no bigger athiests then people forced into Catholicism!)
I should point out that I was raised in the outback and the closest church would have been hundreds of kilometres away. My only exposure to religion was via Quaker missionaries who were trying to convert Aboriginals to Christianity. The Aboriginals didnt like them, we didnt like them, and it was always a relief when they moved on to the next town. ie my experience of religion is very negative. It sounds like you have had a positive experience though, which is wonderful.