Is it possible? Because its not even giving me the option. Am I missing something here? Thanks in advance.

It isnt. It is already enchanted.

I see. I was under the impression you could enchant it. I guess you only could if you had the two enchantment perk thing.. Oh well. Thanks

Nope. Not even then. Extra Effect only works at time of weapon creation.

[edited by TheMFossum because of double post]

Dawnbreaker has a unique enchantment called Meridia's Retribution that deals 10 points of fire damage on impact, and has a 25% chance to make undead explode in a fiery blast upon death. This blast will damage any nearby undead, and can cause any survivors to flee for a short time. Undead killed in the blast will crumble into ash piles. The fiery explosion has the same visual effect and functions as the Bane of The Undead spell.

As you can read from above, Dawnbreaker is already enchanted. It does have a high number of charges, one of the highest that I have seen. I'm sorry to break the bad new to you on this.