There seem to be striking typological similarities between Dravidian and Australian languages (see, e.g., the answers to this question Are there languages with the three-fold articulation place contrast dental–alveolar–retroflex?). There are also genetic studies suggesting an Indian migration to Australia 4000 years ago (see http://www.bbc.com/news/science-environment-21016700).
Is there an attested historical linguistic link between languages of India and Australian languages?
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.
I did some amateur research into similarities between Eurasiatic and Australian as well as Trans-New-Guinean. There is some similarity in numerals for one, two, five and ten (ten usually has part meaning "two" and five often means "palm" or "one palm"):
Besides this, there is a striking similarity in the words for fire, but this hypothesis should be rejected because the word for fire in Australian is known to originate from the word for wood.
Dravidian is often considered Nostratic, one of the closest relatives of Eurasiatic, but I know no similarities between them except the numeral for four (nāl in Proto-Dravidian). In my opinion, this can be a borrowing. There is no similar numeral attested in Australian.
I also have seen claims that Australian and Indo-Pacific (including Trans-New Guinean) are "Eurasian" languages (whatever it means in the author's terminology) as opposed to Austric family from the same region.
So, to sum it up, if Australian and Dravidian are related, I would guess, they are more likely related via Eurasiatic than directly.
