6-8 weeks with any luck.
The main La Nina drives are fluctuating or on the downturn, except for SAM.
Condition could return to neutral early Autumn, the SAM index needs to drop a little, but generally, the major indicators are favourable for a return to drier conditions by end of March.
(SAM is a major influence on east coast rain/cloud though...)
http://www.bom.gov.au/climate/enso/index.shtml