Hey Rem,
Mate you're spoiled for choice here in Cairns, the Capra will be perfect! Enduro bikes are the best tool to get the most out of your stay here, as mentioned before Copperlode is the place to be for raw and technical tracks, there are 6 tracks that drop off from Lake Morris Road (Copperlode), 5 of which are at most 40 minutes to ride up a bitumen road which hardly sees any traffic, with the last being Crystals taking a bit longer, about an hour, but a great ride. Have a search on Strava for the tracks Waddlebla, Slipperies, Cheepies, Scorpion, Boi Boi and Crystals, should give you a good idea the loops and how to get back, if you'd like to swing me your details I'd be happy to show you around, Cheepies, Boi Boi and Crystals are less full on so I'd definitely recommend giving them a crack first, Waddleblah is great besides a very rocky and steep top section of chutes, Slipperies is a cult classic among local downhillers for being a meat grinder, super steep and loose, almost unrideable in the wet, and scorpion is not too bad besides a few steep techy sections.
As for shuttles, Craig at Tropic Rides is the man to hit up, I'd expect with everyone in town for the Champs he'll be running shuttles like mad, he's a top bloke who knows the tracks like the back of his hand, his page is here:
https://www.facebook.com/Tropicrides/
And that's just the tracks off Copperlode, there are so many more options around if you're keen to shuttle as well as 60km of prime tracks up in Atherton, definitely recommend a trip up there if you've got the time. You can't go wrong up here mate, you'll have a ball.
Cheers,
Kyle.
