Hmm, it depends on the style of paladin. The most obvious comparison are the Vigilants of Stendarr who certainly wouldn't touch daedric quests.
In my opinion, there are two types of playable paladin, The Vigilants of Stendarr style - Aedra Good, Daedra BAD, People Good, Undead Bad, but frankly this didn't entirely fit with my own concept.
Personally, I was simply playing a retired soldier looking for redemption for perceived past sins. In my arrogance I judge good and evil, based upon human suffering. I considered myself a Paladin, because I represent the fight against those that would do harm to good people, and especially against those that would desecrate the dead.
Meridia is a Daedra, whose prime hatred is of Necromancy, which is evil. As long as Meridia's goals and the enhancement of human life match, we have no problem. If Meridia were to cause suffering to any innocent or good person, I would have no part of it.
Perhaps I'm not a true Paladin, because I am less a Holy Warrior, but more a magic wielding soldier whose sole purpose is to fight evil. There is a big difference. The difficulty comes when you have to commit evil for the greater good.
From the sounds of your character however, it really depends on their level of sophistication in terms of Philosophy. A true Religious Paladin should be fairly well versed in Philosophy, and scholars are quick to point out that the Daedra are only painted as demons because they are the opposite of Aedra whom we call Gods. Personally, being a Paladin is more than simply saying I am a warrior of God, because the Aedra rarely directly point you to "things are bad", even the concept of all Daedra as evil is largely a Cyrodillic invention.
An Imperial Holy Paladin would probably shun the Daedra, a Nord, Breton, Hammerfell, or Morrowindian may have a more open mind.