Your post is a little confusing to me. You say that you're flying LHR-MAD in the morning, then turning around and flying MAD-LHR-DOH on another ticket. Do you mean that your QR flight was booked to originate in MAD?

In any case, you may struggle with all this. You'd have to drop your very early bags at T4, then get yourself over to T5 for your MAD flight. You may overwhelm the poor person who may not understand why you'd want to check in a bag early for mid-journey later.

Depending on your timings, it might be better to either (i) check it in to the MAD flight as well, or (ii) leave it at left luggage in T5 in the morning and pick it up during your transfer later at LHR.

I don't know what your turnaround timing in MAD is, but I'll just drop in the warning about travelling on separate tickets and the potential dangers and financial implications of no-showing for the next ticket (as you don't have a connection and are not protected.)