I live in Redcliffe, which is just near the Domestic Airport and I pay $280 for a 2 bedroom duplex which has a HUGE yard and they allow me to have 2 dogs, 1 cat & a bird lol. I have done heaps of searching over the last 12 months after separating from the ex hubby and now trying to find a new bigger house. Honestly finding a house that is pets ok is easier than it seems, recently (compared to 12 months ago when i was last searching) there is a HUGE amount of owners now allowing pets in their properties.
I wouldn't live in Carlisle again if the rent were free and I lived there for 5 years (in laws lived their for 12years), same goes for Cloverdale. Redcliffe in some parts is just as bad, I have had people throwing bricks over my fence aimed at my 5 year old son's head.... NOT safe.
Now for the cheapish nice areas that I would live in....
Kewdale (LOVE it, lived there for 7 years and wish I'd stayed there, wont be moving again until I get a house in Kewdale), Belmont (again some parts), Ascot (not often you get cheap there but there have been a few), Midland (some parts), Stratton (just past Midland nice little area), High Wycombe, Forrestfield, Rivervale (Avoid Great Eastern Highway Units etc, always trouble), Guildford, South Guildford, Victoria Park, East Victoria Park, Bayswater, Bassendean, Ballajura, Morley, St James, Bentley, Kalamunda, Greenmount and there are heaps more.
I judge a suburb after either living in it for more than a year or on what I have heard on the police scanner lol.
Another thing your going to need to consider is the costs involved with moving house, normally 4 x times rent= Bond, plus 2 weeks rent in advance, $100 pet bond (most of the time) and 1 weeks rent for the application fee when you first apply (will be credited as part of your 2 weeks in advance rent). So just there on a house that's $280 per week your going to need near $2000 to move.
Anyways that's enough from me lol good luck!