Has anything changed diet-wise? Did she get a new treat or maybe table scraps? Have you changed her flavor of dog food?

I have never heard of vomiting as a symptom of separation anxiety... usually they are just really destructive to the house or themselves.

To be honest, I would bring her to the vet if you can rule out ANY possibility of her getting into ANY foreign substances. Is your trashcan inaccessible? Do you have any potted plants inside? Do you have any cats and an accessible litter box she can get into? My dogs would be sick for days at a time every now and then and I couldn't figure out why until I caught them eating kitty poo... then it all made sense.

But bottom line... if this persists it could be something more serious, or it could just be nothing at all, but bottom line, I would rather be safe than sorry and take her to the vet!!!