Hamad International Airport in Doha has, in common with the other ME3 hubs, several "waves" of arrivals and departures. These are periods with lots of arriving and departing flights, with lots of transit passengers, aimed to give good connections. If memory serves (and you can check on the airport departures board to be sure!), there's one in the morning and another in the evening.
For inbound flights, the origins are divided into two groups, "safe" and "might not always be safe in all cases". That distinction is based not only on the country they're coming from, but also on whether or not the origin airport allows certain kinds of transfers or if all transfers require full re-screening.
If your flight arrives from a "safe" airport, and you don't have a bus-gate (so jetty disembarking), you may (not always) be permitted as a transit passenger to just go straight out into the departures area. (In this situation, transit is straight on, arrivals follow the normal signs up the stairs). If you have such an arrival, you can get from your seat on the plane to the terminal in a couple of minutes, and hence from one seat to another in under 10 minutes if everything lines up!
Otherwise, you need to head upstairs, then walk along to the central transit re-screening areas in the middle of the terminal. If you're unlucky with gates, or have to be bussed to the terminal first, this can take a little while. If you get there at a quiet time (so not during a big arrivals wave), you could be through in a minute or two. If you're last off an A380 when a few other widebodys have just landed, in the middle of a big arrivals wave, you could be in for a long wait... (Hence photos you've seen)
I've had a 90 minute connection, with lucky gates and a "safe" origin airport, where I've had time to have a shower (in the business class lounge) plus breakfast before boarding. I've also had a ~2 hour connection, with bus gates both ends, and long security queues, where I didn't have time to visit the lounge at all, just run to the gate to board. It varies!
However, if you hold a through ticket, I wouldn't worry too much. For very tight connections, they should give you a pass (envelope?) to go through an (often) shorted tight connections queue. Otherwise, I've been on a few long-haul flights which were held for 10 minutes to await late-running connecting passengers. Very worst case, Qatar Airways would rebook you for free on a later flight, and provide a hotel if it was a very long wait. Not much fun if it's only a one-flight-a-day route though!
For a frequent route, booking the shortest connection the website will allow should be fine if you're an experienced traveller who walks fast and doesn't get flustered if things go wrong. Otherwise, 90-120 minutes might be a good minimum, especially if you want a chance to visit duty free / lounge / etc. You probably don't want much more than 2.5 hours there, unless you have lounge access or like shopping. Well, unless you can get closer to 6-7 hours, when the free tours of the city or the (hard-to-qualify-for) free stopover hotels start being an option!