It depends on the context. I have never heard "give me a doe" before, but "give me dough" (if talking about food) could mean that you are literally commanding someone to give you dough to make something with. "Give me dough" could also be slang for "give me money". (Dough= slang for money). Let me know if this helps and feel free to ask me for help anytime. I see that you have edited your entry. That being said, "give me the dough" could still mean either of the things above given the correct context. If it is in the context of money, then yes it would be an idiom.

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"Give me a dough" and "give me the dough" are different. "Give me a dough" only makes sense if you are baking, there are several piles of dough, and you want someone to hand you one of them. Even then, it is a strange sounding sentence. "Give me the dough" means "give me the money." You cannot just use any article in this sentence. They're not interchangeable.