Scottish? Toddler English?

Really, I'm not going out on a limb here, well maybe I am. Tell me what you think.

I got Larien's favorite gown (Care Bears, one of three thanks to the wonderful Mom Mom) the other night. She squeals, "That's me gown."

She does this with other things as well. Sometimes it is "my toy"; other days she says "me toy".

So, what do you think? Are the Scots stuck in toddler mode of speaking?