You might be looking at a couple conditions. HGE (hemmoragic gastroenteritis), pancreatitis, or a mild gastric enteritis. HGE can be caused by a viral infection and is treated symptomatically. Problem is that it doesn't take long for dehydration to set in and anemia from blood loss. If you suspect HGE is the culprit she needs to see a vet as soon as possible, but in the meantime offer her pedialyte or ice chips in very small frequent doses. You might even consider boiled chicken and rice in those same small doses but only if she continues to hold it down. Usually antibiotics and medications for the diarrhea and vomiting are needed to speed recovery. Most dogs with this benefit from a day or so of IV fluids aswell.
Pancreatitis is different but with very similar symptoms of diarrhea and vomiting. It is also very painful and most run a fairly high fever. If this is suspected a vet visit is imminent.
IF she has a mild form of gastroenteritis the treatment above for HGE should help her out while keeping her hydrated and slowly she will be able to be eased into her regular diet.
Avoid in the future sudden changes in diet and table scraps as this is one the easiest solutions to try. She might benefit from a permanent diet change into something that is bland but safe on her tummy. Prescription diets like E/N or I/D are frequently prescribed.
Do you have reason to believe that your pet got into something toxic?
With your dog being 1 year of age the risks of parvo are decreased. We worry about that in young pups and older dogs. He is one which means he probably has been exposed to parvo enough to have developed some immunity. The adoption centers usually do not release pets without vaccinations. Sure it could be parvo but definitely less likely.
You have only had him a week. He has gone through a lot of stress he probably has also experienced a diet change chances are what you are seeing is a result of the above. Keep an eye on him, try the options in the previous post, don't let him get dehydrated and take him into your vet.
Rabies signs usually include the inability to swallow which causes the foaming at the mouth, neurological symptoms (wobbly gait, confusion).
As long as the antifreeze is not accessible than you should be okay. Try the above and see if it helps him.