"Our dog has only one ear."
So it looks like 只 is the mw for 耳朵 because 只 is a measure word for one thing in a pair. Cool!
No, it can be used on things not in pairs. It can even be used on animals, birds, things like boxes, watches, rings, other body parts like hand or foot, to name a few.
Question for you. I am still trying to understand when measure words are required. In this case 狗 did not have one and 耳朵 did. Is the measure word needed when there is a possibility of more than 1,
P.S. there is nothing wrong with your examples
Chinese is specific only when it is needed to be (certainly there are limitations). The Chinese sentence of Duo above also applies in the case where "we" have more than one dog and all of them have only one ear, i.e. "Our dogs have only one ear." It is certainly a bit odd but is nonetheless completely correct. The number of dog(s) is not mentioned and is not important as long as it is/they are our dog(s). You need a classifier when you talk about the quantity, whether you specify it, approximate it, or inquire about it.
One of our dogs has only one ear.
A few of our dogs have only one ear.
How many of our dogs have only one ear?
Lol. It is not perfect (seriously). It should be "我们只有一只只有一只耳朵的狗。" Lit. We have only one dog that has only one ear.