Taylor Swift and Travis Kelce are reunited down under -- and their first order of business as a couple was to go back to the zoo she was just at the day prior ... talk about déjà vu.

The lovebirds were seen hand in hand Thursday walking through the Sydney Zoo -- taking in the sights and peeping all the animal exhibitions. Tay Tay seemed to take the lead in showing him around ... which makes sense since she was literally there 24 hours before his arrival.

The attraction must've left a good impression on her, 'cause she clearly thought it'd be worth taking TK for round 2. Indeed ... she was playing the tour guide, as seen in these sky pics obtained by Australia's Channel 9 News. Heck, Traylor even fed a kangaroo at one point!

Now, they came off like they usually do as they moseyed around ... namely, super in love and tied at the hip. Not only were they holding hands, but they were locked in a hug a few different times as well. So, yeah ... they're still going strong and very into each other.

As we reported ... Travis was en route to Sydney Wednesday after hopping on a private jet Tuesday night from L.A. and making a pit stop in Hawaii.

Now, in terms of privacy ... it doesn't appear Taylor and Travis had the place shut down for themselves -- there were other zoo sightseers walking around, but they did seem to have their own little bubble without being bombarded by fans and gawkers. Thank you, security!

They got a few days together through the weekend -- however, Taylor will be busy ... as she's got 4 shows to do each night simultaneously. Safe to say, Trav will be in attendance.

Ya gotta wonder what else they'll get into ... Sydney's a cool town, and there's lots to see/do. We'll be on the lookout for some bridge shots -- everybody heads there down under.