Would your dog know the difference between "get the door" and "get your ball"?I've seen a few interactions like what you are describing..."get the door","turn the light on"....etc. I also wonder her understanding. One theory is these short phrases like this have been said over and over all her life and over time she knows what the short phrase means. I can tell my dog "get your ball", " go get your baby..ie his stuffed toy"... and he will do it. I wonder if this is similar?
Keep in mind I'm a huge nerd and the little intricacies about how people use language and how we communicate
(get as in retrieve vs the colloquial get as in "do an unstated but appropriate and expected action on the object")
is, in fact, my jam (unlike Priscilla and motherhood).
"Get the door" can mean several different things.
It can mean to physically go pick up a door and bring it from one location to another.
It can mean to go back and close an open door.
It can mean to hurry ahead and open a closed door, potentially to even hold it open so another person can go through it.
To figure out which unstated meaning the speaker intends, you have to analyze your environment, determine the issue, and choose the definition that makes the most sense for the given situation. It would make sense to go pick up an actual door on a building site. It wouldn't make sense to do that while leaving the house, so you need to choose another definition.
Turn the light on means one thing. You don't need to analyze the environment or infer what the speaker means. Make the light come on.
Get the door can mean 3 or more things, and responding appropriately to the request involves a decent amount of awareness and observation. Again, I'm talking like 5 or 6 year old level here, not secret genius level.