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Yes. It has a +1 enhancement bonus. That is what Damage Reduction(DR) is measured against. So if a creature has DR 10/+1, then a Shillelagh spell(or any +1 weapon) ignores it. If it was 10/+2, then it protects against a Shillelagh.
Oh yes. It is a wonderful spell for low-mid level druids. My personal favorite is Flame Blade, though(it gets around ALL DR(although not SR) and is a tough attack).