Even if you are connecting on a single ticket, it would not be odd to have your reroute handled at DOH. While your flight is currently delayed by 2 hours, that could change for the better or you could make up time in the air and land less than 2 hours late. Or your onward flight could be delayed for any number of reasons and you might still make the connection.

While this certainly looks grim, carriers routinely do not rebook until there is a misconnect.

As already noted, if you are not connecting, but have separate tickets, it will be for you to arrange onward transportation and the value of your original onward ticket will depend on its fare rules, e.g., if it is refundable, it may retain value if you no show.

Even if you are on a sinlgle ticket, it always makes sense to do the research and look at options. Simply depending on the late-delivering carrier will not likely yield you the best option. Be prepared to specifically ask for the flights you want.