Are most versions of Superman destined to die fighting a Doomsday in their own Universe? I'd figure some where killed by Doomsday, while some succeeded in killing the monster!

We know the Golden/Silver age Superman never fought one, who knows though if in all the universes brought back by the infinite crisis all the premier Supermen/women fought a version of doomsday. We can only wonder, Those stories haven't been told yet.

Grant Morrsion's action comics run had that Superdoom creature hopping from universe to universe giving The super people trouble, don't know if it killed any of them though. That could've counted as their fight with doomsday if not their literal doomsday like with modern age main earth Supes.

If you want, the best example possible is the New52 Superman.

He fought Doomsday twice. One we were only told about, and the second time we actually saw it. And twice he defeated Doomsday.

Pre-Flashpoint Superman on the other hand... Got killed once and almost killed twice (that I remember of) by Doomsday.

Oh! And he was almost killed by a kryptonite Doomsday that was created by the military using G.I's as human test subjects. He got saved in the very last minute.

I don't believe Earth-22 as shown above ever met Doomsday... EVER! But that cannot be verified since I don't think there is enough backstory to actually know for sure. He did seem to evolve a type of immunity to Kryptonite, and in the novelization of Kingdom Come, he could actively resist magic itself, to maybe he has something similar, though on a weaker scale than Doomsday does.

Gog killed more Supermen than Doomsday ever could.