BA will NOT check your bags through on two separate tickets. Even if you can enter some linking note in the PNR.

This seems to me an extremely risky connection. For example BA2033 landed at 1:25am on 23/12 departure.
Of course, your flights could be on time and you could make it if you rush, but that is cutting it very tight.

There might be a way to to avoid getting through custom/immigration and have your bags directly forwarded to your final destination, once you reach DOH, but I am not familiar with the procedure if any.

ANyway, I would never favor travelling under such a stress.