Sandy, the red eucalyptus doesn't seem to be as aromatic as the eucalyptus you often see in dried floral arrangements. The leaves have a slight bit of the smell, but the wood is really pretty benign. I can go into my shop the day after turning it and still smell it, but it's a different smell that whan you'd think of as eucalyptus. Still might bother you though, if you're sensitive to the eucalyptus smell.
Thanks for the compliment, Barry. This was local wood (from a tree removed at my office). This species is "red ironbark" eucalyptus, and it turns pretty easily when green, but when it's dry it's like concrete. I turn it green, soak it for a day ot two in denatured alcohol, wrap it in a few layets of newspaper, and then let it dry foa about a month. I've not had too many problems with cracking as long as I make sure there is no pith in the piece. With pith it's the pits. (Say that a few times fast.)
Also, the sawn bowl blanks and trunk slices will almost always crack unless they are sealed immediately after cutting. I have a few red eucalyptus log sections that I didn't get sealed well enough, and they've turned themselves into pre-split firewood for the next-door neighbor.