Now we do need to tread with care here since her vomiting is quite profuse and elderly cats are generally quite delicate.
Now as long as her gums are normal, she isn't in pain and toxins can be excluded; we can monitor her until her vet is open. And I am glad to see that you plan to have her seen since her signs do raise worries of bacterial or viral gastroenteritis, pancreatitis, parasites or dietary indiscretions. Though given her age, we also have to be wary of this being triggered by kidney disease, liver issues, secondary to metabolic issues (ie diabetes, thyroid disease), IBD, or even cancer. And while this could weaken her to make her more wobbly, the 2 issues aren't likely directly related.
Now as you monitor her, we can try some home supportive care for her. To start, if she hasn’t just vomited (since otherwise we’d need to rest her stomach for a few hours first), then you can consider treating her with an antacid. Common OTC pet safe options would be: Pepcid (More Info/Dose @http://www.petplace.com/article/drug-library/library/over-the-counter/famotidine-pepcid) or Tagamet (More Info/Dose Here @ http://www.petplace.com/article/drug-library/library/over-the-counter/cimetidine-hcl-tagamet). Whichever you choose, we’d give this 20 minutes before food to allow absorption. Of course, do double check with your vet if she has a known health issues or is on any medications you haven't mentioned. Though if you give this and she cannot keep it down due to nausea that is usually a red flag that we need to bypass her mouth with injectable anti-vomiting medication from her vet.
As we let that kick in, if she is weak and lethargic, we can try boosting her blood sugar by rubbing a sugary syrup (ie glucose syrup, honey, karo syrup, pancake syrup, or even non-grape jam) onto the gums. This will get some sugar into her and hopefully perk her up for us.
Afterwards, you can consider starting her on an easily digestible diet like boiled chicken, boiled white fish, scrambled eggs, or meat baby food (as long as its garlic/onion free). There are also OTC vet diets that can be used (ie Hill’s I/D or Royal Canin’s sensitivity) too. The aim of these diets is that they will be better tolerated/absorbed by the compromised gut. Therefore, it should get more nutrients in and result in less GI upset. As long as improvement is being seen, I usually advise continuing this until the signs are settled, and then weaning her slowly back to her normal diet.
Since dehydration is a risk here, we need to keep an eye on her hydration. To check that she isn't dehydrated, there are a few things you can test. Further to checking for gum moisture, do make sure she doesn’t have sunken eyes and that she doesn’t have a "skin tent" when you lift the skin. To see how to check these parameters for dehydration, you can find a good video HERE (http://www.ehow.com/video_12232503_dog-dehydrated.html). If you are seeing any signs of dehydration already, then that would be our cue to have her seen before this becomes an additional issue for her (especially as it is often dehydration that makes them feel unwell).
Overall, her signs do raise a few worries here. Therefore, you are right to have her seen once her vet is open. In the meantime, we’d want to start supportive care to settle her stomach. And once she is seen, we'd want her vet to assess her hydration, check bloods to make sure her organs are worming properly, make sure there is nothing in her stomach that shouldn't be there or any sinister viruses present. Depending on their findings, her vet can treat with injectable anti-vomiting medication, fluids, +/- antibiotics to get her settled before this can take a toll on her.
All the best,
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