When and where were sprung dance floors first used?  I am looking for
specific dates and venues and full references to sources or some other
form of validation that the data is reliable. Australian references
are of primary interest but info from other countries would be
helpful.

Maybe some of these web sites will provide you with more information.

http://www.gpd58.dial.pipex.com/history.htm

"...In 1909 the King opened the new ballroom containing the first
sprung dance floor in Europe. The first dance he took with the Queen,
and the second with Mrs Keppel.   A medal was struck to commemorate
the event, and the King allowed the royal coat of arms to be used to
publicise the establishment."

http://www.msdance.fsnet.co.uk/hist.htm

"...In his advertisements of February 1906, and other publicity for
the this new venue, Mr Brewin had speculated as to who would have the
first dance on the new sprung Dance Floor"

http://www.npg.org.uk/live/history.asp

"Three adjacent buildings on Orange Street were converted by Alex
Murray and Neil Morgan of Grimley J.R. Eve: Ciro's Club, a 1960s
office block and an 1840s town house on the corner of Charing Cross
Road. Ciro's Club was designed in 1915 with a sprung-floored dance
hall and had been leased to the Royal Dental Hospital from 1956 until
1985."

http://www.stoddardnh.org/nathanmorse.html

"...This large house with its imposing portico with balcony across the
front was built by Nathan Morse who carried on his shoe business in
the shop next door to the west  which later became the Stoddard
historical Building. Nathan lived in Stoddard 1828 until 1854 when he
died. Ellen, one of his eight children, lived on there for many years.
Mr. and Mrs. Robert Webster owned the house in 1974.

The house has the distinction of having a large, sprung dance floor on
the third floor with benches around the sides for those sitting out
the dances in the 19th century..."

http://www.nwlink.com/~smithwri/fleet/floors.htm

"...Mountaineers—Seattle 

Built in 1950 by folks in the mountain climbing community, the
Mountaineers building at 300 3rd Ave. West in Seattle has two
ballrooms, with maple dance floors. The larger floor in the Olympus
Room is 4,000 square feet and is "sprung"—the joists rest on springs.
It features a large stage, 20x25 feet and four feet above the floor,
that can hold a small orchestra. There also is a balcony around the
dance floor..."