Sydney Sweeney's floating on cloud nine ... not only did she got Instagram official with Scooter Braun -- but she took a high-flying tour of a famous bridge Down Under.

The actress was spotted in Sydney, Australia, Sunday taking The Harbour Bridge climb ... a tour where patrons can walk along the underbelly and enjoy breataking views of the city's famous harbor.

Sweeney -- who was joined by her father Steven Sweeney and her pal Kelley McCartney -- had to strap into a harness to safely walk across the bridge ... and she and Kelley stopped to pose for a few pics on the way.

It seems Sweeney's feet are barely touching the ground these days -- not only is she touring tall landmarks, but she also sat on Scooter's shoulders at Stagecoach in one of the photos she posted to hard-launch their relationship on IG.

Obviously, we know they've been dating for months ... but, she only just went official on social media -- an important step in modern courting -- with Scooter.

Worth noting ... Scooter's not down in Australia with her, as far as we know -- but we don't think he's far from her mind.