Will Australian Hibiscus grow in the dappled shade under a large gum?
Sorry to tell you that this plant needs lots of sun - you could try it if the gum is tall and with sparse foliage - but you'll not get the best from it.
Your Native Hibiscus, Alyogyne huegelii, foliage will be a bit thin and it will not flower as heavily as if it had full sun.
Here's a link to the Plantfinder page:-
https://www.gardensonline.com.au/GardenShed/PlantFinder/Show_1616.aspx