You are certainly allowed more than one stopover @ LHR, and I have personally had an itinerary with 2 such stopovers.
The rules concerning stopovers are
- travel may not be via the point of origin (and so by implication no stopover there)
- maximum two stopovers in the continent of origin (which for you is Asia)
- minimum two stopovers required
That's all

with regard to the LHR-DOH-LHR being flagged, an outside possibility is that this a hangover from an old, old version of the rules which restricted the number of intra-Europe/Middle East flights to/from the UK. I consider this unlikely because it would have had its own specific error message.

But it can be easily checked - simply change LHR-DOH-SYD to say CDG-DOH-SYD.

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FYI the old rule was removed by the update of 2016-12; its wording was:
4(h) A minimum of 3 and maximum of 16 segments, including surface segments between any 2 airports, are permitted for the entire journey.
Free flight segments within each continent are limited as follows:
Africa 4
Asia 4
Europe Middle East 4*
*not more than 2 of which may be between the UK and ALBANIA, ALGERIA, BULGARIA, CROATIA, CYPRUS, GREECE, MIDDLE EAST, MOROCCO, ROMANIA, RUSSIA west of the Urals, TUNISIA, TURKEY, UKRAINE
...