The Driftwood-1 exploration well is located in 99 metres of water in permit WA-320-P.
Quadrant's environmental plan application to NOPSEMA said a jack-up drilling rig would be deployed, along with a support vessel and helicopter.
The estimated total duration of drilling is 32 days and the well, which is a commitment well, may be drilled any time up until 31 December 2017.