I feel for you. There's nothing worse (OK there is, but you know what I mean!) than signing up for a frequent flyer program, only to find you can't then book the awards you want.
Living in Australia, it's hard not to fly Qantas on an award sometimes. They can be, depending on route and time of year, very difficult to nab.
All of the airline programs are different. It's up to them how many awards they make available, how much they "cost" etc. That's competition and you vote with your feet. That's why I'm AA EXP and QF nothing. For me it's about the miles I earn and how many I need for the awards I want with One World in general. It "costs" a lot more to earn an award in the Qantas program than with AA for example.
As it costs so much more for a Qantas FFer to earn an award (in most situations), it makes sense that QF gives them priority. Your own award partner tends to treat you better than the competition (may make an award available - but I don't think QF do that often/ever in F, possible upgrades on their flights etc) depending on your status with them. NB it depends on status - you need to fly with them rather than transfer points from a credit card etc.
People pick the FF program that's right for them and take the pros with the cons! If there was the perfect program for everyone we'd all join!
Of course, this is all too late for you but you can always change for next time!
Have you joined the Qantas FF program? The last time I looked it was free and that way you can look up their award availability online. It can change from day to day as they adjust for loads/ other commercial considerations.
BTW - Welcome to flyertalk.