Do you know what kind of scorpion it was?
If not what state do you live in? (So I can check for what is in your area)
Is your dog experiencing any of the following symptoms?
DroolingTearing from the eyes (the animal looks like she is crying)Inappropriate urination and defecationDilated pupils
Muscle tremorsBreathing difficultyCollapse
Well the good news is only one Scorpion in Arizona is dangerous to the point of being medically concerning. Though any sting can result in a medical emergency with your dog as she could be allergic. That would be the Bark scorpion.
Any sting should be reported to your vet asap. Mainly because the dog could be allergic and could die without treatment. What I would suggest is taking your dog in today regardless. Your vet will want to examine the sting and watch for the above symptoms.
As for the stinger, no it does not have to break off in order for the scorpion to inject the venom.