Wirelessly posted (Nokia E61 Wi-Fi 3G GPRS: Mozilla/4.0 (compatible; MSIE 6.0; Symbian OS; Nokia E61/0633.09.04; 9730) Opera 8.65 [en] UP.Link/6.5.1.3.0)
No.
If you're transferring to a domestic QF flight you could use the shower in the domestic Qantas Pub (err Club).