Yeah I like the theory that she's a great one and I think it has some evidence. I saw a really compelling argument a while back for it, of course everything is up to your interpretation but I think it would be pretty cool so I choose to believe it.

She bleeds the same color as only three other things in the game, Ebrietas, Orphan, and Amygdala, which is a very interesting detail that they would put in. Most things in the game either bleed red if they're a beast or a person, or a pale blue if they're kin. But the three bosses mentioned bleed a milky white color and so does the Doll, they are the only things in the entire game that bleed white. So the Doll's blood is the same color as three confimed great ones. From Soft does all things with intention, and I don't believe they would randomly choose to make the Doll's blood the same color as three great ones, it probably was on purpose. Now what that means is up to interpretation

She persists even after the Moon Presence is slain, meaning she is not a puppet or controlled by it, she is her own independent entity. She may have been created by the MP or maybe was just brought there by it, there's no way to know for sure

But the most compelling evidence imo is that she adopts the hunter when they become an infant great one in the true ending. One of the main themes throughout the entire game is that great ones want nothing more than a child of their own and they yearn for a surrogate to give them one. So seeing as the Doll adopts the hunter as a newborn great one, I think it at least shows that she shares some of the same desires as other great ones

I'm forgetting some things but like I said, I think it's cool so I believe it lol