It seems nobody has answered the question yet and I think it is an interesting one. What does it actually mean to say "You're out a dollar?"
Is there any definition of "out" that could make this sentence make sense? "Out," used as an adverb, makes reference to a place. "Out here. Out there. Where are you going? Out a dollar." No. That's obviously not right.
The adjective almost makes sense, except that the subject of the sentence is you. "You're out." Makes sense so far. That's like saying "You're gone." So let's apply that. "You're gone a dollar." That doesn't make sense to a native English speaker. Why doesn't it?
We don't write it this way in English because if we want to convey that it is the dollar that is gone, not the person, then we must make the dollar the subject of the sentence.
You could say "Your dollar is out." Although, this requires further explanation to specify from where your dollar is out: "Your dollar is out of your possession." Of course, to a native English speaker, that feels a bit cumbersome and redundant since we know it can be conveyed more succinctly by simply saying "You've lost a dollar."
"You're out a dollar" sounds like poor English for poor people. If you wish to say something like this in the future, just say "You've lost a dollar" like a grammatically correct English speaker.
Edit: English learners - I maintain, do not use this phrase if you intend to speak English properly. Go ahead and search for the phrase with quotes "out a dollar" and you will quickly discover that this is not a common phrase. In fact, this question is currently the top search result for me because it's such an uncommon, incorrect use of English.
Edit: After a lot of discussion and downvotes, I am still not convinced that the phrase "You're out a dollar" is grammatically correct. Please be aware that this is in fact a slang phrase and, while you are welcome to choose to use it, you deserve to know that is slang. It is not recommended if you are going to be using it in a formal setting.
I'm sorry people are having trouble understanding this, but the phrase is slang. I'm astonished that anybody familiar with the English language would insist that it is grammatically correct. It's not.