Dream and point of reference

Hello all, I was wondering about dreaming and narrative reference. In the last chapter of Through the Looking Glass, Alice wonders if it is she who dreamed the red king, or if she had been a player in his dream. The narration at this point is in the third centered upon Alice, then this curious poem is attached to theend which seems a break in narrative continuity, at least in this final chapter. I believe it's fairly easy to sya that the poem is written from the perspective of the red king, and that he is dreaming of Alice. Furthermore, this calls into question, at least in my mind, the fact of reality about Alice to begin with (I've noted posts joking that she needs therapy, but is that still true if she's nothing but a dream figment?). I know the poem is an acrostic for the name of the real alice, but I still wonder about the point of dreams and how Carrol seems to point out that it's not so much that she had the dream, or that someone else had it and she happened to be there, but that it was had at all, and experienced. Thoughts?