Thank you for the detailed response @rajkamalmohanram. Since India doesn't allow dual citizenship will I be allowed to fly out with two passports from the Indian airport in case if my family manages to courier me the Canadian passport to India? Anyone here who was successful at that?There is risk involved IMO.
The safest way is to apply for a Canadian passport + Entry visa to India and then travel. If this trip is not for an emergency, postponing it would be the best course of action.
There are some flaws in your plan. Entering a country with one passport and exiting it with another passport might invite trouble. When you are coming back, you will be entering Dubai with your Indian passport and leaving with your Canadian passport? That might cause problems. Usually, you enter and exit a country with the same passport.
Alternatively, you can apply for a Canadian passport in India but exit India with your Indian passport and head to Dubai. When you land in Dubai, show your Canadian passport and get visa free entry and then fly onward to Canada.
Another thing that might work is if someone can collect the Canadian passport in Dubai and mail it to your Indian address. That way, you can probably show your Indian passport when exiting to Indian immigration authorities but when you land in Dubai, you can get a visa-free entry with your Canadian passport. Once you enter Dubai with your Canadian passport, you can then exit and leave for Canada with the same passport.
Also, can passports be couriered internationally? I heard it cannot be. I need to do some research here. Thanks again.