Gosh, I've used 4 auto doors this last 6 months. 1 uses plug in electricity and that seems to help. 1 tries to offer options and combines settings; has to be defaulted and reprogramed multiple times to sort out. "RunChicken" has been simple and reliable but has too small an opening. I've recently installed the ADOR2 turkey door. At 12.5" X 20" it works perfectly. The problem I had was 2 ducks would try to enter at the same time, start to get stuck, then back up a few inches, squabble at each other, and then decide they didn't want to go in after all, just sit down blocking the other duck from entering. Like watching a cartoon; hope you have sensible ducks.
The 10.5"x12.5" may be OK if installed just right with a little height. Not sure about some of the drakes but a 10-12lb duck should be OK. I think with the low power requirements for an auto door, even a small battery and a 5 watt+ solar charger should work. As others have said, you'll want someone to check the door daily when you go on vacation.