Yes Kay you seem to be right. However I have a distinct recollection of a tree like this in my childhood growing rapidly from a small stick my father planted in the ground. This was from before the Eucalytus was commmon over here (1950s) The tree grew throughoutr my childhood until it was higher than the house. I thought it was willow, but my father said it was mountain ash. The leaves looked identical, but there was no perfume when you break them (like there is with eucalyptus). Maybe a smell test would verify?
TYhe leaves of this tree were weeping in habit and I remember the leaves sometimes developed a strange red eliptical bubble about the size of a baked bean, when I popped rthem opened they seemed vegetavble to me but my father said they were some form of bug. You got usually one per leaf and I dont recall them bustring open.

If it smells of eucalyptus it is a eucalyptus of course.