Swift wore a plunging floral midi dress and tan heels, and her beau wore a navy shirt and dark wash jeans.
A source also tells WHO that the couple has been "very friendly" to the staff at their hotel, as well as the Hiddleswift lovers that have gathered outside.
"They have encountered fans inside the hotel several times and have been very gracious," the source added.
Hiddleston, 35, played coy, however, when a reporter grilled the actor about his "girlfriend" before he headed out for a Swift-less jog on the beach with his trainer.
When asked how Swift was enjoying Australia, the actor laughed and said he didn't want to answer the question. He said, "I don't know," when asked what they were looking forward to doing on their trip.
Swift and Hiddleston met in May at the Met Gala, and started dating shortly after Swift's 15-month relationship with DJ Calvin Harris ended that same month.