tivolitheatre

On the 1907 25" OSI map at GeoHive. Google Streetview. The Corn Exchange facade at the extreme right is still there.

Opened as the Tivoli in 1901, finally closed in 1930 per arthurlloyd.

Originally built in 1843 for Daniel O'Connell's Repeal Association per archiseek

Several entries under different names in the DIA in this general search for Burgh Quay.

Niall McAuley Thanks Niall - added a grand brace of tags from your links.

The Tivoli Theatre's construction began in Albert Street, Brisbane in 1914, on the site of the former Turkish baths.[1] It was designed by architect Henry E. White in an art nouveau style and could house 1800 people on three levels. It was chilled by an air plant that could pump ice-cold are through the venue. It had ruby red carpets. It also featured a garden rooftop theatre holding 1200 with open sides for ventilation and steel shutters that could keep out the rain.[2][3] Its facade overlooking Albert Square had Oriental influences.[1] It opened on 15 May 1915[4] and featured a production of The Tivoli Follies in the auditorium and a vaudeville production in the rooftop theatre. These were staged by Hugh D. McIntosh, a showman, and promoter who was influential in the Rickard Tivoli circuit of Australia. It had a rival in vaudeville theatre the Empire Theatre also located in Albert Street which drew bigger crowds.[5] Smoking was permitted in the rooftop theatre. During Brisbane's hot summer months, the rooftop garden was meant to be more desirable. As the building had two entrances, it was possible for two production companies to co-exist on site with separate audiences as well.[1] Films were later shown in both venues after the advent of talking films. Union Theatres Ltd. renovated the Tivoli Theatre in 1927 using Sydney architects, Kaberry and Chard. This was to provide for more seating as the venue changed from a live theatre venue to that more suited to a film-going audience. Two galleries were removed to make way for a single dress circle.[1] With the onset of the Great Depression in the 1930s, it was critical that the theatre could accommodate enough people to recover costs from cinema audiences as live theatre attendance dropped. More renovations to the foyer and the auditorium took place in 1935. The Tivoli was purchased by the Brisbane City Council in 1963 and closed in 1965. The intended King George Square development led to a number of buildings being demolished, including Centennial Hall and the Hibernian Building.[6] Programs from the theatre are held in the Fryer Library of the University of Queensland. Source: en.wikipedia.org/wiki/Tivoli_Theatre,_Brisbane

Explanation of the Word “Music”

From the Greek “muses” who were the 9 daughters of Zeus and Mnemosyne. As legend has it,
the muses had no individual attributes for a very long time and they equally patronized every
form of music and poetry. The muses only developed individual characteristics in the 4th century
B.C.
The 9 Muses are:
1. Calliope—Patron of the epic poem
2. Clio—Patron of history
3. Terpsichore—Patron of light poetry and dancing
4. Melpomene—Patron of tragedy
5. Thalia—Patron of comedy
6. Polyhymnia—Patron of lyric poetry
7. Erato—Patron of elegiac poetry
8. Urania—Patron of astronomy
9. Euterp—Patron of Music
The Greeks word for museum, mouseion, referred to a shrine with priests and sacrifices that was
centered on a cult for the muses.

Source:
maxwellmuseum.unm.edu/sites/default/files/public/World%20...

The exotic dancer in the photo is most likely playing the role of a muse, named Terpischore a patron of light and dancing. As explained in my previous comment. I could not discover the identity of the dancer, yet at least there it seems she performed in Tivoli theatre in a role originating from Greek mythology.

Also, it seems the word is spelled as Terpischore rather than Terpoichore, as the writing on the photo also confirms.

In Greek mythology, Terpsichore (/tərpˈsɪkəriː/; Τερψιχόρη, "delight in dancing") is one of the nine Muses and goddess of dance and chorus.[1] She lends her name to the word "terpsichorean" which means "of or relating to dance".

Terpsichore is usually depicted sitting down, holding a lyre, accompanying the dancers' choirs with her music.

Terpsichore was also said to be the mother of the Sirens (including Parthenope) by the river-god Achelous.

Source:
en.wikipedia.org/wiki/Terpsichore

trove.nla.gov.au/newspaper/article/146569389 - Table Talk, 12th April, 1923...possibly the same dancer here...