Operator Arc said it started drilling the well on Friday morning using the Century-18 drilling rig, which for the past three weeks has been undergoing a planned maintenance.
Drakea-1, which is about 19km southeast of the Dongara township, is being directionally drilled to target the High Cliff Sandstone near the structural crest of the prospect.
"If Drakea is a success there are a number of follow-ups in the onshore Perth Basin which look quite similar," Arc managing director Eric Streitberg said.
The well is expected to intersect the top of the sandstone at a measured depth of 2589m, or about 495m north-northeast of the surface location.
Drilling is expected to take 16 days to reach a total depth of 2839m.
Arc and Origin are 50:50 partners in L1.