I went to a grocery store yesterday with my friend. When we were almost done with the shopping we noticed a pile of watermelons without a pricetag. And I said:
"I don't think it goes by the pound. It goes by the unit. Maybe I should ask one of the store clerks for the price."
I think it is a bit too odd to refer to a whole watermelon as a unit. Although I probably could get my meaning across, I want to know the proper way to say. What would you have said if you were me?
Usually, I hear it called "by the piece," other dialects may have other forms. The term "unit pricing," the way you used it is perfectly acceptable; I say it myself on occasion.