Did you know that if you are lucky enough to live in a zone warm enough to grow lovely scented Eucalyptus that you can propagate them easily by simply taking a cutting of a new twiggy growth and placing it in a glass of water, or in a light weight potting mix to root?
It can take four to six weeks for new roots to begin to show.
The best time to collect clippings from a Eucalyptus would be Spring or Early summer when new growth is semi-mature.
The best method is to dip the cut end in some rooting hormone to encourage rooting and then place it in a light weight potting mix to root.
Good luck!