I did this exact thing in 2009 except I had 1 more hour than you (3:30p to 11:00p). I was also making a domestic connection so I didn't have to clear customs either way.

It's definitely do-able but as others have said it is a hassle or expensive (or both!). Unless things have changed in the last 3 years there isn't any great inexpensive way to get to the CBD. Taxis are expensive and the bus takes forever.

I was unemployed so I took the bus (also, the queue for the taxi was about 75 people deep!). It was kind of fun to see the locals and listen to the dialects, but it took over an hour to get to the CBD. Once there, I walked through King's park and down some trails to the Swan river, where there is a walking / cycling trail. It was a beautiful day, and I really enjoyed it (WAY better than the airport lounge...). I then had a couple pints before heading back to the airport.

On the way back I took the bus again, and some older Australian drunk lady yelled a bunch of racial slurs at an Indian girl, then some other younger people screamed at her. So that was pretty entertaining.

In short, I say go for it, if you are adventurous. You won't have time for a nice dinner but you can see something worth seeing. I think you'd need a taxi at least one-way, it will help you a lot with time and comfort, if a bit more boring. But if you want to try the bus on the way to the CBD it may save you some waiting for a taxi and you'll see a little slice of the 'regular' Perth.

Thinking about it now; I am certain I didn't have my bags with me, but no idea what I did with them. There must have been lockers in PER somewhere.