G'day mandibee
Looks good but at today's currency exchange your 40 quid is worth roughly 62 dollars Australian so maybe u can do it but depending on your means of travel and dietary expectations and accommodation should not be too bad be aware some backpackers can be dumps and expensive even as a back packer but you should be fine here in oz food and fuel are the two main expenses every one complains about budget airlines are a really cheap way to get from point a to b quickly and saves money if you book online you can pay as little as your daily budget to get to say Sydney to Adelaide where a bus would take you 2 days, as you have allowed 30 days less the week in Sydney it does not give you much time to see the sites we have just spent 17 days alone in the west of the country and we saw very little of it mainly Perth and down south and then up to Broome, your friends in Sydney may help you plan your stay.
Also be aware Australia is still suffering form some localised flooding so some of the places you may wish to visit will be affected.
Have a really good time and as we say here in oz haveabloodygoodweekend

and don't forget the aeroguard for mozzies.
Cheers Stewart