Alternatively if I were to just enter Qatar without entering transit area and then take uber to the souq and do the shopping/dining there, is it possible to go cashless and just depend on credit card?
Credit card ok for using Uber and dining and the vast majority of shops. But maybe not all of them in the Souq. Also regular taxis don't take card so would have to stick to Ubers.
So probably for 90% of the time a card would be ok. However, I would suggest having at least a small bit of cash. Either get QR100 from an ATM or pay for something from an airport shop in another currency and get the change back in Riyals?