Where you obtain the ores is irrelevant, and can be obtained from either another player, the Grand Exchange, purchasing from the Dwarven ore store in the Dwarven Mines underneath Ice Mountain and Falador, or by mining the ores yourself (level 15 Mining is required for iron ore). You can mine these ores in any mine that produces these ores in the game.
Be wary of travelling into the Dwarven Mines, as there are aggressive scorpions (level 14) and a few aggressive King Scorpions (level 32) that will attack you in some parts of the mine. Be prepared to fight them, or flee from them if your combat level is low, should you travel into some parts of the mining area.
For a "safe" area to obtain all of these ores, you can also travel to the mine at Rimmington, directly south of Falador.
When you have all the ores needed, return to Doric to finish the quest. The ores have to be unnoted or Doric will not accept them. If you have the ores with you when you start the quest, simply talk to Doric again after he asks for the materials.
Upon the completion of this quest, one's Adventurer's Log will read: "Who says you don't get rewarded for doing favours? I can now use Doric's anvil whenever I fancy."
Doric used to say that he uses his anvils for making amulets, even though they can't be made on anvils by players.
Because of the ability to collect the ore before starting the quest, the quest could be considered one of the shortest quests in Runescape.
With the release of the Behind the Scenes article for October 2012, Jagex revealed that they would be replacing Doric's Quest with a new quest that would have "low-level requirements, [with] post-quest orders for high-level smiths to complete". On 17th October, Doric's Quest was replaced with the What's Mine is Yours quest.