Commentary:
Genuine thing the original comic does very consistently for a long time -- it's always hard to tell how those linguistic constructions change over time, but she always calls it the "home" and refers to Warbucks as her "daddy," in quotes, and that, to me, reads, well, the way she suggests here.
Text summary: (click to open)
"How did you know?" Our Annie asks the younger version of herself.
"It was pretty obvious," the younger Annie responds, like it genuinely was the most obvious thing in the world, "I recognised myself from the mirror, of course -- and you call it the "home" in airquotes just like me!"