Hi Susie, we did look at renting (in the Brisbane area) and it pretty much is 'yes to all of the above. We had no rental history either. You will have a whole bunch of forms to complete which gives you a chance to explain that. You also have to detail your income revenue, or how you will be able to meet the rent. Your completed forms are sent to the home owner who will decide on who will be accepted.
Our experience is that there is a big demand for rental properties, and when you go to an open viewing there are generally quite a few other viewers. Having said that apparently it is easier from February for a couple of months (but by then we had decided to house-sit instead. The dogs won't be a problem, in as much as properties descriptions will state if pets are allowed (some may stipulate that they should not be in the house). Finally, when you get to the house often they bear little resemblance to the photos (this is same buying properties as well). Mostly they are out of date, with furniture photoshopped in, and the room sizes and decor are not quite what they seem.
Although this all seems quite negative this is just our 'take' on it, so good luck with your property hunt.