You live in the Great State of Arizona, as I have for 50 years (wow, I can hardly believe it!). I also owned a gun shop in Arizona, and am very familiar with the gun laws here. There are no restrictions on private transfers in Arizona (only the federal requirement that both parties be residents of Arizona). In other words, wrap the gun in a well-decorated box and leave it under the tree for her, you need not go through any "official" channels, transfer through an FFL, do any paperwork, etc.

BTW, it has been a long-standing tradition in my family to give guns for Christmas, which started in about 1959 or 1960 when my Mom gave my Dad a Colt Python for Christmas (she put it in a huge heart-shaped See's Candy box, reallly surprised Dad! Back then, NOBODY could find, let alone buy, a Python). Let's see, a few years later, my parents gave me a Weatherby Mk V in .300 Wby Mag for Christmas (yes, that was a good Christmas!), and many others were given between my family members. I suggest you wrap that gun in a candy box, or something similar, to give her a real surprise, neither of you will forget it.

Merry Christmas!