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That details depend a lot on whether you can get an online boarding pass from Pegasus.
As a transferring passenger, the first thing you do in Doha is to clear security again before you can get enter the main terminal area. I don't recall what documents they check at this point but it is likely that you will need a boarding pass at this time. Once you are through security you can just walk to your gate.
If you don't have a boarding pass, you will have to go through immigration and customs, enter Qatar and go to the Pegasus check in counter.
I would call Pegasus and ask. Unfortunately these days check-in procedures are fairly unpredictable depending on what Covid document checks are required and who will do them when and where. Most airlines can do doc checks at both the check in counter and the gate, but in Doha you may not be able to get to the gate without a boarding pass.
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Assuming Indian citizenship
Qatar allows visa-free 30-days to the country for Indian, so, assuming you're respecting the COVID regulations, you don't need a visa (you can't qualify for transit Visa as :