You are not going to make that connection, period.
Your bags will NOT be checked through, because United and Qatar do not "interline" bags (technically there are different kinds of "partners"). United used to interline with Qatar, but United ended their interline agreement with the Qatar and 4 other major Middle East airlines as of May 2017 (this was apparently part of a snit that the major US legacy airlines threw because they claimed the Middle East airlines are too heavily subsidized by their respective governments, so United, American and Delta have been stamping their collective feet and complaining to the US government; when that didn't get them anywhere, they started making things more inconvenient for their customers - this end to interlining is one result of that). So you will have to do the bag drag and all the extra time consuming hoop jumping that requires.
The term "minimum connection time" (or MCT aka a "legal connection") is a misnomer. It does not mean that's all the time you will need to make your connection. It's what the airline's computer program thinks will work on a good day under ideal conditions, so they can sell you a ticket. There are no days when conditions are ideal if you're connecting between 2 different non-partner airlines at LHR from Doha to Chicago with checked bags.
I think you need to execute your Plan B.
You also need to fire that travel agent, who is pretty clueless and is not doing you any favors.
Now, all that said, there is one potential way this might resolve itself...but it's a gamble and depends on two things beyond your control (both would need to happen):
- One of your airlines having a schedule change between now and your flight, which would tighten your connection time even more - this is quite possible if your flight is not for many months. Airline schedules shift constantly, and if your connection shortens, your airline should be willing to rebook you on a different flight (in fact, potentially a much better one) if you ask; and...
- The airline's CS agent is willing to do that for you. They frequently will. But there's no guarantee of that. If, as you say, you have some status with United, then it's nearly a sure thing they would accommodate you.
If it were me, I'd look into Plan B (but I'd also look into what "better options" might appear if there's a schedule change in your favor).