I am based IST, I think there is enough time. Do you have Star Alliance Gold card or Business Class Ticket? If so, immigration is much faster with fast track options.

The immigration que on IST is based on luck, it could be empty and done in 5 mins, or could take up to 30.

If your tickets are seperated, which I assume it is because Pegasus and TK is not alliance, then you have the take your luggages, leave immigration, exit to arrival area.

If I remember correctly, direct heading to Domestic is from Left, but I think you have to go up level for departures, choose elevators, then move left. No need to exit terminal.

I dont understand why you need to leave checked luggae to facility? You will not take them with you for flight? That process can loose you time, If you have the luggage allowance, take them with you directly to Izmir.

Pegasus has online check-in, from T72 to 60minutes before flight, and If you are going to check-in luggage, than you had to be at check-in desk 45mins before flight.

If you are not going to check-in bags, you can directly go to security and to gate, which is all the time you have, until they close boarding. You can use Pegasus App for Mobile BP, works with QR code scanning while boarding at gate.

Once I left my home exactly 1hour before flight, arrived domestic terminal 20 minutes before flight, had online QR Boarding Pass, no luggage, straight to security & gate, even had 1 cookie while people were boarding, entered as last passennger.

Pegaus is also famous with little delays, so you will have couple minutes advantage while they are on the hub of TK

I think everything should go well and there is enough time to be at check-in desk at pegasus before 19:15 which will make you safe.
If only cabin luggage for pegasus, even time for coffee

At worst case, there is 4-5 airlines going to Izmir everytime daily for cheap fares from IST.

I would not change anything, go for it, you can make it without stress and do the Online Check-In definetely, better before your TK flight.