If you're after a classic chip shop style hamburger, there's a fish 'n' chip shop called Kameruka Seafood in the small shopping centre at the corner of Beaudesert Rd and Kameruka St. (where the Night Owl, Domino's Pizza, Subway, etc are).
They only opened late last year, but I've had their works burger, plain burger, and steak burger a few times, and they've been good every time. Good chips too, but the serving size in the meal deal is a tad small. The burgers are a decent size, though.
Alternatively, there's Jack's Cafe near Coles in Sunnybank Hills Shopping Town, which is right next to Calamvale on Compton Rd. Their burgers are pretty good, but I'd say Kameruka Seafood is a little better. Plus the wait time at Jack's has been pretty long both times I've been there. Still good though.
One place I've yet to try is the Fish King Cafe at Calamvale Marketplace, cnr of Beaudesert Rd and Nottingham Rd. Pretty sure they do burgers as well, and have been meaning to give them a shot.