There is no evidence of a linguistic link between Dravidian languages and Australian languages and I haven't heard of a proposal for 'Dravido-Australic' superfamily. Typologically the groups of languages are quite distinct although of course comparing two groups of languages is always going to generate lots of similarities between individual languages.
Taking Tamil as the canonical Dravidian language, it has a phonology which is quite different from Australian languages, having numerous fricatives and affricates (famously absent from almost all Australian languages), and a large set of approximants. Tamil also has many more vowels than Australian languages, which typically have 3.
While Tamil is superficially similar to Australian languages in grammar, both being agglutinative, it is much more so than Australian languages and can string together large sequences of suffixes to produce very large words.
But as commenter @TKR points out, the comparison of the present-day languages, whether of phonological inventories or the grammar, are not useful as evidence of ancient connections as they would have changed substantially since that time.
Australian languages fall into several quite distinct families. The largest one, Pama-Nyungan has had some reconstruction work and the results do not look like Dravidian languages. As well, proto-Pama-Nyungan is usually given a time-depth of around 5,000 BP, so it is too old to be connected to Dravidian languages at 4,000 BP. And of course proto-Australian (if there ever was such a thing) has a much greater time-depth.
As for the Indian connection of 4000 years ago, that was a finding in one genetic study, others have had different results, including a divergence between Australian and South Asian Y chomosomes of around 54,000BP. And of course Indians have been present in SE Asia for over 1,500 years, while over the last few centuries there has been regular contact between peoples of SE Asia (Macassans in particular) and Australia, so an Indian genetic link could have been brought to Australia that way. But even if an Indian genetic link was substantiated, evidence about a linguistic link is a quite separate matter.
To summarise, a Dravido-Australic language superfamily has not been proposed because there is, at present, no evidence of such a connection.