Vera Pauw's team held the co-hosts scoreless in the first period but conceded a spot-kick on 52 minutes, which Arsenal defender Catley smashed into the roof of the net.
Ireland responded to that set-back by being more daring in their approach play and put the Australians under a lot of pressure, especially late on, but they could not find that goal to level matters.
This Group B opener was always going to be a tight affair so it was hardly surprising that the crowd of 75,784 fans had few clear-cut goalscoring chances to get excited about.
Australia took a few shots from distance but never truly troubled goalkeeper Courtney Brosnan, while Katrina Gorry showed her class in periods as she kept Ruesha Littlejohn and Denise O'Sullivan on their toes.
Ireland had a couple of half chances with Kyra Carusa and Marissa Sheva causing panic at times and captain Katie McCabe was constantly shutting down counter attacks and sparking her own team's surge forward.
After Catley converted the penalty, Australia rallied for a few minutes and pushed Ireland back. But that only got the Girls in Green fired up and they started to wreak havoc with Heather Payne excelling on the right flank.
A Louise Quinn header late on almost sealed a draw, while McCabe and Payne could have made a better connection with attempted efforts. That goal that their positive display merited never came.
Ireland will now travel to Perth to take on Canada on July 26h.
Australia: Mackenzie Arnold; Ellie Carpenter, Clare Hunt, Alanna Kennedy, Steph Catley; Hayley Raso, Kyra Cooney-Cross, Katrina Gorry, Cortnee Vine (Emily Van Egmond 75); Caitlin Foord, Mary Fowler (Clare Polkinghorne 85).
Ireland: Courteny Brosnan; Heather Payne, Louise Quinn, Niamh Fahey, Megan Connolly, Katie McCabe (captain); Sinead Farrelly (Abbie Larkin 63), Denise O’Sullivan, Ruesha Littlejohn, Marissa Sheva (Lucy Quinn 63); Kyra Carusa (Izzy Atkinson 88).
Referee: Edina Alves Batista (Brazil).