There are several things you want to do to prepare. I assume you already visited the Day of the Gods pedestal and won the local challenge.

[1] Hire a piper and a chaplain, they will cast heroism and bless on your entire party.
[2] Acquire 3 bows (the fourth you will find in the dragon cave!).
[3] Accept Mr. Malwick's wand.
[4] Buy the Fire Aura spellbook at the Initiate Guild of Fire, and enchant your bows.
[5] Cast Wizard Eye and Torch Light.
[6] Visit the Haste pedestal.

Now you're ready. Enter the cave in turn-based mode. There are three battle phases.

[7] While the dragon is dealing with the rats, use Mr. Malwick's Wand of Fireballs on it. Don't kill the rats. Grab the fourth bow and enchant it with Fire Aura. Leave a single charge on the wand so you can recharge or sell it later.
[8] As soon as the dragon turns its attention to you, go into real-time mode. Now keep shooting your arrows, but make sure to step aside each time Morcarack starts to breath its breath. This takes some practicing. Save after you dealt some nice damage and reload from there if things go wrong (once you have gotten good at this, you won't need to reload often). Occasionally there is time to go turn-based and do some healing, if necessary near the entrance where it may not be able to reach you.
[9] When the dragon is close to death (say some 100 hitpoints left), kill it in melee combat. This way you'll end the fight much quicker and you will finish before the haste spell runs out.

Now the job is done. Save and
[10] Loot the body, reload if you feel like it (I normally just accept what I get) until you're happy. Have fun!

The task can be made a little easier if you buy a Recharge Item scroll at the Magic Shop. You will have enough charges to rely on the wand to complete the job, no need for heroics with the bows!

There he lies flattened again, the poor sod.