This problem has hit me as well. If we're not qualified to do a quest, then don't let us take the quest. If we're looking for available quests, only mark ones we're qualified to complete with the standard quest icon and others with the red "unavailable" icon.

Not only, as Rhagnar points out, is this standard in most MMOs, but it's even the most common pattern here in FFXIV. The biggest problem is that it's not consistent. There are some quests that don't allow you to take them until you're qualified to complete them, and then there are others that let you accept them, do the objectives, and then only when it reaches the turn-in step does it become "unavailable". (There's several quests in Camp Drybone that act that way, for instance.) It's annoying.