Sound's like a plan to me. If something unexpected happen's,it is simple to revise. Unless you tap return,some air need's to somehow flow from basement to room above. A hole in door leading to basement will surfice. So will a hole in floor/ceiling between basement and room above.

Well I am a little nervous because this has to be done before drywall goes up, and once it goes up, I can't get to the ductwork anymore. Although I will be adding a little access panel to get to the damper, so I guess I could always turn off the damper and that would revert the system to what it is today

Adding a single supply register in the basement is unlikely to affect the rest of the house. I would suggest to not cut off the duct running to your daughter's room, but install a damper with the access panel so it can be opened and closed as needed. If your basement is like mine, you will be closing the register in the summer. Even a single register makes my basement too cold when the AC is running.

I will be adding an access panel so I can reach the damper that will be suppling that duct.

We don't want air going up that duct into the daughters room, it has 2 ducts because the homebuilder messed up and ran the duct up the wall that was meant for the master bedroom but was to far over and ended up in the side bedroom and they just decided to leave it because home builders are idiots.

I am thinknig about now adding a T to the duct and having 2 supply registers to even out the airflow a little bit