Hello & welcome, I am Dr. B, a licensed veterinarian and I would like to help you with your wee one today.
I am quite concerned about Rosy, especially if she is so nauseous she cannot eat and has both vomiting and diarrhea.
Now as I am sure you can appreciate, just like people, dogs can have GI upset with vomiting and diarrhoea that is caused by a range of agents. These include bacteria viruses, parasites, toxins, foreign body ingestion, and general dietary indiscretions. (Though in Rosy's case, toxins and dietary indiscretions are hopefully less likely at her age. That said, if there is any chance she could have eaten something she should not have, then we'd want her checked urgently). It can be daunting to get to the bottom of which differential is to blame and with her signs sounding so severe we do want to be proactive here and not let this go on too long (since dehydration is a risk and that will be what makes her start to feel poorly with this).
Once that has had time to absorb, you can consider starting her on a light/easily digestible diet. If you do so, start with a small volume (a spoonful) to start. Examples would be cooked white rice with boiled chicken, boiled white fish, or scrambled eggs (made with water and not milk). There are also veterinary prescription diets that can be used in cases of gastroenteritis (ie Hill’s I/D or Royal Canin’s sensitivity). When you offer that spoonful, give her 30 minutes to settle. If she keeps the food down, you can give a bit more and so on. As her tummy stabilizes, you can offer more. The aim of the easily digestible diet is that it will be better tolerated and absorbed by the compromised gut. Therefore, it should get more nutrients in and result in less GI upset. Also by feeding this in small frequent meals, it will reduce diarrhea volume. As long as improvement is being seen, I usually advise that the diet be continued until the diarrhea is settled, and that they are then slowly weaned back to their normal diet over a week. Since vomiting and diarrhea can quickly dehydrate a dog, even as she is drinking, we need to keep an eye on her hydration. The reason is because no matter how much they drink, we often find that dogs just cannot keep up with diarrhea fluid losses for long (and dehydration is what makes them feel poorly). To check her hydration status to make sure they are not becoming dehydrated there are a few things we can test. One is whether the eyes appear sunken, if the gums are tacky instead of wet/moist, and whether she has a "skin tent" when you lift the skin. To see how to check these parameters for dehydration, you can find a wee video on this HERE. If you are seeing any signs of dehydration already, since she is older, then you do want to have her seen by the vet before this becomes an additional issue for her.
If you are concerned that she is becoming dehydrated, you can try and encourage her to drink but offering fresh water or even low-sodium chicken broth. Furthermore, you can offer rehydration solutions like Pedialyte. Pedialyte is nice (though aim for a flavorless one) because it will get some of those lost electrolytes back into her as well. Do note that you should not give this via syringe if her vomiting doesn't settle first. If it does, then you may and a typical maintenance rate for hydration in an animal is 48mls per kilogram of weight a day. Of course, her requirement will be higher since we'd have to also consider how much fluid is being lost but this is a good starting point. And of course, if she were to vomit when you offered fluids via syringe, you would need to stop (since we'd not want to cause vomiting with out intervention).
Furthermore, there are some anti-diarrheals that can be used in dogs to slow things down for their gut if her stools are very runny. As I am sure you appreciate, these would not be a cure (since cures would depend on the culprit and might include antibiotics or anti-parasitics, etc.) but would slow the diarrhea to aid the body potentially absorb more water/nutrients then it would have if the diarrhea were unchecked. Furthermore, these treatments will coat the GI and could just settle the GI upset. In regards to safe options for your wee one, the one we most commonly use in dogs is Kaolin/Kaopectate (More Info/Dose) or PeptoBismol (More Info/Dose) available from your local pharmacy. Furthermore, Protexin Pro-Fiber (which is available OTC at vet practices; example) would be another option. All will slow diarrhea and the Pro-Fiber has the bonus of providing support to the delicate good bacteria of the GI.
Overall, GI upset of this nature can be triggered by a wide range of agents. Therefore, we'd want to consider supportive care to settle her stomach at this stage. If you try this over the next 24 hours and don't see improvement or she is appearing dehydrated, then we'd want to consider getting her vet involved. If you need to do so, consider taking a fecal sample with you so they can see what is producing and potentially have it tested if need be. Depending on the exam +/- any fecal test findings, her vet can treat her with an injectable anti-vomiting medication, antibiotics, +/- appetite stimulants if need be to address this for her, settle her stomach, and get her back to eating for you.
I hope this information is helpful.
If you need any additional information, do not hesitate to ask!
All the best,