Maybe your neighbour just loves babies and wants to be friends? She might have picked a bad time to try and instigate a relationship, but she seems well meaning.
Maybe things are different over there, but here, when you have a baby, every tom, dick and harry shows up with a cake or some other kind of food after a baby is born. It's the way we go about showing we care and want to help in a small way.
I remember my Aunty B telling me a story about how, after her daughter was born, my Mum made her a sponge cake and delivered it on the second day, and how my aunt said that cake was just about all she ate for the first few days and how she'll never forget how glad she was to have it.
My point is that different people and families have different customs. Sometimes they seem odd, but mostly they're harmless.
Try not to be so weirded out by her. She sounds pretty harmless to me.
