When you go to check in desk, if you show your AU passport to show that Australia would let you in, what's the problem here?
I'd think it might be a problem at the check-in as well. The OP has not indicated if he/she has a valid Indian visa attached to his AU PP AND has mentioned that the Indian PP was used to enter the country.
When one approaches the check-in desk, the PP is scanned to retrieve the trip details, personal details, etc. So in this data retrieval, the pax's AU PP will not show any valid Indian visa. So this raises the question, how did the pax enter the country in the first place? Again, this MIGHT NOT be a concern for outbound pax, but, the check-in agent would have doubts ?
Additionally, at the immigration desk, when the AU PP is scanned, the corresponding inbound date will not come up and so the questions could be ;
1. Did you use this PP to enter the country?
2. If no, do you have a OCI booklet that was used? Note that the OCI booklet is digitally linked to the overseas PP.
3. If no, then how did you enter the country?
We have to note that all airports in India, DO stamp the inbound stamp on a travel document AND this stamp is verified physically as you exit the immigration area. It is expected of (although not written/documented anywhere) the pax to ensure that the right date is stamped (often during midnight arrivals into the country and the date might have moved to the next calendar day)
Also, on scanning the AU PP, there will NOT be e-visa that is linked. Even if the pax was at some point an Indian national eligible to apply for & be issued with an OCI/POI AND if the pax did not acquire OCI/POI card, then the pax should have a valid visa issued & attached to the foreign PP.
My reco, would be to exit India on the Indian PP and pay the fine when applying for OCI in AU. Last time I checked it was around $100ish or so per use of Indian PP after acquiring foreign nationality.