Please be aware that Melbourne has multiple airports and that these results are for all airports serving the city.
The best day to arrive at Melbourne is Friday and it would be best to avoid Thursday, as prices are on average 158.5% higher than on Friday. (Average prices, based on 208 datapoints.)
The cheapest airline flying from Melbourne to Perth is JetStar Airways. They are 47% cheaper than Qantas. (Average prices, based on 200 datapoints.)