I use doTERRA Oils on me and in my business in diffusers to help calm the grooming environment. 
From doTERRA site: Eucalyptus trees are tall, evergreen trees that grow up to 50 feet in height and are sometimes referred to as Gum Trees. The main chemical components of Eucalyptus radiata are eucalyptol and alpha-terpineol, making it an ideal oil to promote feelings of clear breathing and open airways and for creating a soothing massage experience. Eucalyptus oil has purifying properties that can be beneficial for the skin and for cleansing surfaces and the air. Studies have shown that Eucalyptus oil is effective in helping lessen tension. Eucalyptus essential oil can be found in mouth rinses to freshen breath and promote oral health. Uses Combine Eucalyptus oil with Lemon and Peppermint oil in a spray bottle and use it to wipe down surfaces in your kitchen or bathroom. Add one drop of Eucalyptus essential oilto moisturizer and apply to skin for revitalizing benefits.While showering, place a few drops in the hands, place over nose, and inhale deeply to invigorate and promote vitality. Directions for UseDiffusion: Use three to four drops in the diffuser of your choice.Topical use: Apply one to two drops to desired area. Dilute with a carrier oil to minimize any skin sensitivity. Cautions: Possible skin sensitivity. Keep out of reach of children. If you are pregnant, nursing, or under a doctor’s care, consult your physician. Avoid contact with eyes, inner ears, and sensitive areas.
"Many essential oils, such as eucalyptus oil, tea tree oil, cinnamon, citrus, pennyroyal, peppermint, pine, sweet birch, wintergreen, and ylang ylang are toxic to pets",