| Depends what you you mean by "correct". There are 2 competing classifications of the Coolabah. Until recently it was regarded as a single but highly variable species, known by its earliest validly published name Eucalyptus microtheca F. Mueller. But in 1994 the foremost eucalypt botanists Hill & Johnson published a taxonomic revision in which this entity was split into 8 species (Hill, K D & Johnson, L A S, Telopea vol. 5(4):743-771). In Hill & Johnson's scheme the name E. microtheca is retained but is scope is narrowed to trees from the far north of Australia, in Queensland, the Northern Territory, and just across the border into Western Australia. This is because the type specimen was collected by Mueller on the Victoria River in what is now the northwestern corner of the Northern Territory, and the narrowed circumscription of the species must include the type. In subtropical eastern Australia, where 'Waltzing Matilda' originated, the species recognised in Hill & Johnson's scheme is E. coolabah Blakely & Jacobs, published in 1934 but treated subsequently as a synonym of E. microtheca. It is divided into 3 subspecies. 'Waltzing Matilda' was penned by A B Paterson reportedly while visiting a sheep station at Winton in western Queensland and after hearing a local legend. The subspecies in that region is subsp. arida - or to give it its full name ... Eucalyptus coolabah Blakely & Jacobs subsp. arida (Blakely) L. Johnson & K. Hill. I believe Hill & Johnson's revision of the coolabahs is generally accepted among Australian botanists, though some of their other eucalypt revisions have aroused controversy (e.g. recognition of Corymbia as a distinct genus). | 
