Look for small muffin-shaped capsules among the leaves.

the capsules are not ready to harvest until they turn from green to brown or grey. look carefully at the top (flat) end of the capsule if they are opened up/split apart the tiny seed has already been shed. if the capsules are unopened, take a bunch put them in a paper sack and place them in a warm dry place indoors for a week or so---hopefully the capsules will then open and you can collect the seed from the sack. they can then be shed on top of a seed-starting medium (do not cover) and kept in a warm moist environnemt (indoors) and should sprout in about a week. they are qenerally quite easy to start but may be difficult to grow on outside as tiny seedlings are tender to cold so will probably have to be kept indoors their first winter. BTW, gunnii is fairly easy to get from nurseries especially online nurseires like forestfarm in williams, oregon it might be worthwhile to consider getting a "ready-made" plant rather than going thru the complete seed raising route. good luck.

Hardiness of gums varies quite a bit even within one species. You might want to try seedlings of this locally proven individual.

Eucalyptus sp.- Locks... This tree
has been growing at the Carl English Botanical Gardens at
the ship canal locks in Seattle for decades. It is 60 ft. tall,
graceful and billowy with small, very slender leaves. It does
not match the name on its label, E. dalrympleana, but no one
can quite identify it. It may be a hybrid, but seems to come
true from seed. We thought others should have a chance to
grow it

Here is a link that might be useful: Colvos Creek Nursery Catalog 2010