Actually your transit is nowhere near similar to the OP, but that does not mean you cannot have some time experiencing one of the business class lounges at Doha.
First you have a two hour transit and are not familiar with the airport. Next you are arriving and departing during a peak time where the lounges are quite full. You are also not familiar with each of the lounges which can be quite spread out. You could arrive at a bus gate which can be a ride as much as 20 minutes. You might be lucky and not have security but add another 10 minutes to that.
My suggestion is that when you land ascertain where your departure gate is. If it is A, B, or C (accessible to both lounges), the original business lounge in the south node by the huge Teddy Bear (Al Mourjan) is your lounge. If you have have bus gates with high C numbers you can still use this lounge. If your departure is from D or E and all of C including bus gates in C (because it's in the middle), the Garden Lounge will work better.
Personally I've found the Garden Lounge in the north node to be easier to navigate. And if you have two hours in peak time you may agree. Many on this forum prefer it as the better lounge. I personally prefer the original lounge by the Teddy Bear.
Having said that my last visit was during the other morning peak time where I used AM south. I found a seat, had coffee and relaxed a bit. Did not attempt food. And then found my way to the gate.
If you want to enjoy the experience, familiarize yourself with the layout of the airport.