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MCT is one hour at Malpensa so by rights Qatar probably won't through check bags. Normally they would on separate tickets so long as MCT is respected, BA won't do it in the reverse direction.
As hand baggage only it is perfectly possible to do this, there is a transfer route via airside, and it won't take more than 15 minutes to do it gate to gate, so in theory you even have a bit of lounge time. But as ever any but the shortest of delays will mean you're up for the consequences of a lost ticket and no come back. So it's all about what Plan B looks like.