Went to Mitre10/Bunnings and  bought a box of 5 14g*75mm hex head lag bolt. It has some unscrewed length on the top, but being 75mm long I see no problem. Removed the rubber seal, added a washer, drilled 3 3.5mm pilot holes on the wall (because my smaller bits are too short) and drove the screws in. It felt very tight and secure. :D :D

Thanks for the help. You guys are all great!!

（By the way, the Zircon stud finder is very good.)