Perhaps I'm weird, I prefer to deliberately engineer longer connections when I can. Perhaps that's down to my risk-averse anxiety trait, a trait that's become more pronounced as I've aged.

If the OP booked through BAH online rather than over the phone, one drawback with this approach is that sometimes not all valid connection options are shown on the website. I don't know where the OP is going, but some destinations like BKK have a number of daily options. Certainly on an LHR-DOH-BKK return trip, I called up BAH rather than doing it online for precisely this reason, arranging a generous buffer. However, it does mean you have to do a bit of donkey work yourself, either with ExpertFlyer or ITA Matrix for example, and getting your ducks in a row before calling up.

(Another reason to engineer a longer connection time is if you find the original flight arrives hours before your hotel's check-in time: I'd rather spend a relaxing time in the airport lounge than find myself wondering around a hotel lobby for hours in sweaty clothing).

I am sure 45 minutes is doable even with security, but personally speaking I'd find myself stressing myself out about it, and that's even with the benefit from the knowledge of connecting at DOH at the very least a couple of dozen times.

In the meantime, I congratulate @DYKWIA for manging to squeeze in a drink in the lounge on a 50 minute DOH connection!