Australia is notorious for its ability to remain clean of plants and animals not part of the local flora and fauna, at least until humans started using aircraft and motorized boats to spread invasive species. An advanced species should be able to recognize this quality in Australia.
What you do is relocate all of the sentients to Australia and start your sterilization on the rest of the world, including the sea's so no water wildlife can carry the disease. You map the way the water flows around Australia and how any medieval ships would float and sail when leaving the land. Put warning mechanics like bouys in the water to monitor potential threats and use scouting aircraft and motorized boats to patrol any land medieval ships might be able to reach. Any ships that do not turn back upon seeing your aircraft and ships with a potential "godly" display of sounds and lights, you blow them to pieces with incendiary munitions to make sure any disease is dealt with. Preferably this is done while leaving witnesses who can keep the fear of going beyond Australia's sea's alive. You could make this message even more clear by monitoring important ports for potential long-range sail missions and when you spot one you rain godly death on such expeditions as they are leaving port so the story of why you shouldnt go out to sea spreads like wildfire and you reduce the chance of spreading diseases.
You can also monitor bird migrations before you land, allowing you to exterminate birds that might carry diseases. Especially from Australia most birds will move across the island chains. You could set up large poisoned food and water sources with the purpose of killing birds that attempt to migrate away from Australia. Besides poisoned food you could use small anti-air installations that target birds and ring the edges of the islands with them. You can use sattelite imagery to track flocks and then send boats or aircraft with an overkill on bombs to massacre them as well, you can even capture a few birds, infect them with a virus and release them to kill off most of the species in a viral attack. Between all those methods the non-sentient animals wont stand a chance at spreading the disease.even if a few do reach the mainland they will likely starve as they meet your sterilization program.
For small things like spores and bacteria in the air you are already going to be using methods to clean the air, so you use those to deal with any that come off of Australia. Otherwise your best bet would be building a habitat on the moon, sterilizing earth completely and then replacing the sentient populace you've sterilized and introduced to your own cocktail of approved bacteria and viruses.