EucalyptusBotanical Name Glacier Eucalyptus Plant Type Evergreen tree shrub Mature Size 24 ft in containers Up to 12 ft outdoors (with time) Hardiness Zones 8 11 Native Area Tasmania 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.