I guess it depends on the congregation, but that sounds fairly standard for many congregations, across denominations.
FWIW I attended a Unity congregation for a while, and I was able to keep my children with me if we wanted. Everyone was very welcoming and sweet to my family. My girls usually preferred to go to the children's rooms, since that was more fun for them, but not always, and my toddler was generally with me the whole time.
If I knew there was going to be a meditation (where quiet was very important) I would either take him to the nursery or simply go out with him and come back when it was over. I also sat near the doors so that I could exit discreetly if it seemed he was going to be disruptive. (I still do this at any church or gathering where there is a speaker, actually.) I think if you take little precautions like this, and people sense that you are aware and considerate of them as well as your child, it makes having your baby being part of things pleasant for everyone... and even if there are folks who - due to being unused to children around - are disapproving at first, they'll come around pretty quickly! Unity people tend to be very compassionate and warm, so I'd assume that.
The person letting you know about the nursery also was probably not meaning anything at all, but trying to be helpful and welcoming to you. It's hard going to a new congregation and not knowing where anything is or what is available, and many parents prefer to have their babies in the nursery. Unless it was said in a really snarky way, I'd assume it was just their attempt to be kind. A warm, "Thanks so much, that's good to know! I think she needs to stay with me today," is totally appropriate.
I would love to attend this church but I am not comfortable leaving dd in a nursery at the age of one.
