I have a 9mth old Shih Tzu Poodle mix dog. After waking up from her nap she was drooling a lot. This never happen before. She has a underbite could that be the reason. I just started dogsitting a friend's dog would that have anything to do with this?

Look inside its mouth if you can get it to open it up - There could be something stuck that the dog cannot get out itself - Grass or what not can get stuck and cause excessive drooling,

If this is not it - Try to remember what you have been feeding them, drooling can be a sign of dietary distress and many people don't realize what they should and should not feed their dogs Heres a link make sure your not feeding him any of this I was - www.peteducation.com
As you mentioned it could even be because you are dog sitting if he is more active then usual or could have a little puppy love going on and she could just be more excited then usual

Sinse the causes of sudden drooling can range from a chipped tooth to poisoning,it's a good idea to call your vet right away.Dental problems are the most common cause of drooling in pets that don't normally salivate heavily.The cause could be  a gum infection,a loose tooth or anything that causes pain in the mouth.More serious is the risk of poisoning-from household chemicals,for example-of which drooling may be the first symtom.Drooling also may be caused by rabies or other diseases.So if your pet is suddenly drooling and not acting like his usual self,call your vet immediately.

So Call a Vet or Hopefully its something stuck in her teeth