Head Butt definitely counts all of the damage you deal, including critical damage, strength modifier, and any special modifiers such as sneak attack. In order for a creature to take damage, it must first be dealt damage.
As for how Damage Reduction interacts with this ability:
Some magic creatures have the supernatural ability to instantly heal damage from weapons or ignore blows altogether as though they were invulnerable.
The numerical part of a creature's damage reduction (or DR) is the amount of damage the creature ignores from normal attacks.
If damage is being ignored, it's still been dealt. While it doesn't come right out and say it in so many words, why would it make the distinction to point out that damage dealt is instantly healed?
To be a bit of a rule-lawyer here, I'd only consider the damage "dealt" to be reduced if the rules had read:
The numerical part of a creature's damage reduction (or DR) is how much the damage dealt is reduced by when the creature is hit by damage it can ignore.
Also, just read the entire Combat section. Attacks and spells deal damage, and there's no mention that the damage dealt is reduced by any spells or special abilities (that is, damage is always dealt first, then mitigated afterwards).
Attacks are pretty easy to resolve in most cases. First, you must hit your target, overcoming armor class, hit penalties, then you deal your damage, and then that damage is resolved, including absorbing damage, reducing damage, applying harmful effects, and so on.
As a real-life analogy, head-butt a wall hard enough to break through it, if you can. I can pretty much guarantee that you'll take some damage in the process.