If my father has a dorsal hump and I do as well, will my hump/nose grow to be the exact same size as his?

The size and shape of the nose does tend to be inherited from our parents.  Whether your nose will be exactly like a parent is uncertain until your late teen years.  In addition to that, traumatic injuries to the nose can make the hump worse. A rhinoplasty could certainly remove the hump and by releasing the depressor septi muscle, can prevent the tip from drooping when smiling.  

Hereditary features like a dorsal hump on the nose can be all or none or some combination of the 2. Therefore in your case the hump could end up being the same, larger or smaller than your father's. The only thing that one can say for sure is that whichever option becomes the real situation will be readily evident by your late teens. That is if there is no hump by the age of 19 it is highly unlikely that there will ever be one.