1853 Mueller was appointed government botanist for Victoria by Governor Charles La Trobe in 1853, a post that was newly created for him. He examined its flora, especially the Alpine vegetation of Australia, which was previously unknown. He explored the
Buffalo Ranges.. In the same year, he established the National Herbarium of Victoria, which can still be visited today. It has many plants from Australia and abroad, many of which were collected by Mueller. Also, his large private library was transferred to the government of Victoria in 1865 and is incorporated into the library of the herbarium in Melbourne.
1855–1856 Mueller was then nominated as the botanist to accompany the North Australian Exploring Expedition (1855–1856) led by
Augustus Gregory, and decided to join despite initial hesitations. He explored the
Victoria River and other portions of North Australia, was one of the four who reached Termination Lake in 1856, and accompanied Gregory's expedition overland to
Moreton Bay. Mueller found nearly 800 species in Australia new to science, such as
Macadamia ternifolia (named after his friend and colleague,
John Macadam). In 1856 he published
Definitions of Rare or Hitherto Undescribed Australian Plants.
1854–1872 From 1854 to 1872, Mueller was a member of the Victorian Institute for the Advancement of Science, which later became the
Philosophical Institute of Victoria. He was president of the Philosophical Institute in 1859 when it received a royal charter and became the
Royal Society of Victoria. He was an active member of the society's "Exploration Committee" which established the
Burke and Wills expedition of 1860. Mueller promoted the exploration of Australia, and as one of only two members of the Exploration Committee with any experience of exploration, he made several speeches to the society on the topic. He did not favour the selection of
Burke as leader, but due to factionalism in the committee, he had little say in the establishment, provisioning, or composition of the exploration party.
1857–1873 From 1857 to 1873, he was director of the
Royal Botanic Gardens, Melbourne, and not only introduced many plants into Victoria, but also made the excellent qualities of the blue gum (
Eucalyptus globulus) known all over the world, and succeeded in introducing it into the south of Europe, North and South Africa, California, and the extratropical portions of South America.
1873 By 1873, influential Melburnians were critical of Mueller's scientific and educational approach with the Royal Botanic Gardens. Development of the gardens with an eye to aesthetics was sought. Mueller was dismissed from his position as director of the Botanic Gardens on 31 May 1873. He had done much to develop the gardens with the scarce resources at hand. Though his pay was not affected and he still continued as the government botanist, he never lost his sense of grievance over losing the position. In April 1873, Mueller had created the genus
Guilfoylia and described
William Guilfoyle as "distinguished as a collector [who] evidenced great ardour" and held high hopes for his collecting ability. Mueller's opinion changed when Guilfoyle was appointed to take his place as director of the Botanic Gardens in July 1873. He accused Guilfoyle of being a "nurseryman [with] no claims to scientific knowledge whatever" and of getting the job due to being related to the wife of the responsible minister. Mueller subsequently abolished
Guilfoylia as part of the genus of
Cadellia in his botanical census of 1882 (today the genus
Guilfoylia is again accepted). Guilfoyle went on to landscape the gardens in an aesthetic and pleasing style welcomed by most Melburnians. ==Recognition==