Unfortunately, you cannot legally take them from the wild in NSW to keep them. It also requires an import/export licence to transfer them from one state to another. They should definitely not be released into the outdoors, including a backyard pond, in case they are carrying the devastating frog chytrid fungus and introduce it to a previously uninfected area.
As these froglets have not fully metamorphosed yet, their patterning is likely still developing. That, and the sheer number of species found in the region, makes it difficult to try and narrow down the possibilities. They lack expanded discs on the ends of the digits, one finger is particularly long, as is one toe, and they appear to lack any webbing between the digits. The pupil seems to be horizontal (rather than vertical) and the eyes are not excessively large or bulbous. My best guess would be either the Spotted Grass Frog (L. tasmaniensis) or possibly the Barking Grass Frog (Limnodynastes fletcheri). As far as I can determine, Spotted Grass Frogs can be kept in SA.