First, that is good news to hear that her breathing rate is normal and her gums are pink in the non-pigmented regions (as this is telling us that she is oxygenating normally). With those aside, I have to say that hair usually is digested (as its mostly protein) or will pass mixed in stool. So, with how long ago Zoe had this, the chance the hair is involved is quite low unless it has been sitting in her stomach for the past week. Though if that were the case, you should have seen hair in that most recent vomit.
With that all in mind and knowing that she isn't the kind of dog to have eaten any other odd items, we'd not be overly worried here and can initiate some supportive care. To start, if she has nausea, then we'd want to consider trying her with an antacid (ie Pepcid (More Info/Dose @http://www.petplace.com/article/drug-library/library/over-the-counter/famotidine-pepcid), Zantac (More Info/Dose @ http://www.petplace.com/article/drug-library/library/over-the-counter/ranitidine-hcl-zantac), etc). As well, since we have signs of throat irritation, you could even use OTC Milk of Magnesia (0.25-0.5 tsp every 8 hours). 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 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.
Once that has had time to absorb and she is steadier on her stomach, you can put her on a soft and easily digestible diet like cooked white rice with boiled chicken, boiled white fish, cottage cheese, 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.
Finally, if she is coughing quite a bit and further to the Milk of Magnesia, you can also try her with a mild cough suppressant. Pet safe options we often use are Glycerin/honey cough syrup (with no drugs in it) or even plain honey. Both can be very soothing and can be given at a dose of 1-2 milliliter (~1/4-1/2 teaspoon) as needed. Alternatively, we can use Robitussin DM. Of course, if you use this, we only want to use this one with Dextromethorphan +/- Guaifenesin. Avoid similar syrups with pet toxic drugs (ie Paracetamol, Acetaminophen, Pseudoephedrine, Phenylephrine or caffeine, etc). Dose-wise, you can give 1/2 (half) teaspoon per 10lbs of body weight every 8-12 hours. Again, these can reduce throat irritation and coughing for Zoe.
Overall, none of the signs you have reported suggest an emergency situation for Zoe. As well, with the length of time that has passed since eating that hair, we'd not be overly suspicious that it is to blame here. Therefore, we'd want to try symptomatic treatment to soothe her stomach and throat just now. If we can settle this for her, we are happy. Though if it lingers by the time her regular vet is open, we can consider a check at that stage. They can make sure that stomach is empty and use injectable anti-nausea medication +/- gastroprotectants and anti-inflammatories to get her settled and back to normal for you.
Please take care,
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