EucalyptusBotanical Name Eucalyptus Pulverulenta Plant Type Evergreen tree shrub Mature Size Indoors 26 ft Outdoors 3060 ft (tree form) Hardiness Zones 8 11 Native Area Australia Water your new eucalyptus regularly to prevent their leaves from drooping and falling off. Once established, eucalyptus is partially drought tolerant and does not need as frequent waterings. Very fragrant. Caution: Toxic to cats and dogs.