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Drooling can be a symptom of a tooth problem but it can also be a symptom of nausea. Licking is also a sign of nausea.
If you suspect gums or teeth look into her mouth for discoloration of teeth and swelling of gums in an area. Sometimes teeth can fracture below the gum line where you can't see it. Do a finger sweep around the teeth as well to feel for any particles stuck between the teeth especially if she is eating the rug. If the teeth are discolored it is best to have your vet check them.
If she is eating the carpets when you are not home or she is separated room you n the home then you may be looking at separation anxiety. However if you are finding she is doing this when you are home then it may be pica and this can be due to a physical ailment.
Here are causes for Pica http://www.petplace.com/article/dogs/diseases-conditions-of-dogs/stomach-intestine-liver-or-pancreas/pica-in-dogs