If you're brand new to essential oils, you might be most familiar with eucalyptus through a vapor rub used when you have a cough. Eucalyptus, camphor, and menthol are the active ingredients in VapoRub, giving it that medicinal odor. Eucalyptus is more of an aromatherapy essential oil than a perfumery one- who wants to smell like a medicine cabinet?
That said, there's more to fragrance creation than just making perfumes, and it's useful to know how to use all sorts of materials. If you decide to make something like soap, you'll start to realize you're limited partly on the chemistry of the product. Cold process soaps can alter your scent, and some scents might not be strong enough to be worth putting in them. Hot process involves flash points, since an oil with a low flash point might not survive the heat, meaning you wasted that oil (I actually got into anise when playing around with hot process). Liquid soap (the kind made with oils and potassium hydroxide) can also react in weird ways with different essential oils. Different scents can thicken it or thin it out, some can cloud it, and others might clump up weird. So if you're interested in essential oil blending for products, there's definitely a lot more going on than just figuring out what smells nice together.
I haven't used eucalyptus in soaps, but there are a lot of products you might want to use it, especially if you're feeling kind of sick. You don't want to smell like eucalyptus all day, so you could try it in a salt or sugar scrub, or perhaps put it in a shower fizzy tab so it releases the scent into the steam. Try mixing it with peppermint to make it fresher, or try some lemon for a sunnier scent. Use eucalyptus in your home made cleaning products for an aromatherapy boost.
Since I am mentioning the aromatherapeutic uses, I would like to note that it's advised not to use this oil for children under ten, including sniffing it out of the bottle or from an aromatherapy inhaler. Because there are many different eucalypti, some may be safer for children than others.
And if you really want it in your perfume? Try finding eucalyptus absolute from the stores below for a less medicinal fragrance.
There are a lot of eucalypti out there, and if you can't stand the odor of one, you might want to try another. I've listed some below that I've seen before. There are many more, but this list includes some common ones plus a few that have a bit of a fragrant twist.
Eucalyptus macarthurii - rosy, Arctander notes that it's a eucalyptus for perfumers
Eucalyptus dives - minty
Eucalyptus citriodora- citronella-like
Eucalptus staigeriana - lemony
Other eucalyptus notes:
Cajeput (Melaleuca cajupti or Melaleuca leucadendron)
Niaouli (Melaleuca quinquenervia)