I ride 5 days a week from nedlands to the CBD. Have it down to around 10-12 mins on the way in and around 15 on the way home depending on how lights work and what the wind is doing. You quickly learn that wind is gay.
I only do around 15km on the actual commute, but usually ride to manning road along the fwy bike path and back to bump up the average.
Get a proper road bike (
TBE have them from $950), some clip ons and the padded bike shorts. Its always good overtaking the full lycra fags whilst wearing a bintang singlet with backpack. Also get a speedo that does all the basic things, should only be $30 or so.
A good average to aim for is ~30km/h over the duration of the ride, you won't have it first time out but its something to aim for. Then gradually increase your target average and you'll get fitter faster.
The DPI have a few maps that show all the cycle paths around perth, have a look on google for it as it helps knowing where to go, most retards on the roads don't notice cars so you can get cleaned up pretty easily.