Good evening everyone

Newbie in the forum and non native English speaker so please excuse any unclarities arising from that.

I am planning on flying
London to DOH on the 18th of February 2020
DOH to ZRH on the 24th of February 2020

The relevant part of the itinerary is the London to Doha flight.
I was originally planning on taking the ~2pm flight out of LGW because it is the cheapest but then I saw that I can get an Economy Saver for only 40 pounds more out of LHR on the –3pm flight (QR8 so to have the Qsuites for the potential upgrade).
I have 35k Qmiles laying around that I will probably not use otherwise so I think this is my one chance to use them for an Economy to Business upgrade for the London to Doha leg.
The required Qmiles are 40k from Saver or 30k from the Eco Value fare. (So either book Value directly or buy the remaining 5k needed to upgrade from Saver)
Before I book the flight out of LHR I was wondering how I can find out whether an upgrade is available or whether someone here is so kind to do that for me (I saw that happening in other threads even though I don't know how that works ).
If I won't be able to get an upgrade for the LHR to DOH, I rather book the LGW flight because it is cheaper and also for me the more convenient airport to get to.

I appreciate any kind of information or help you can give me.

Cheers
Philipp