So, the short answer is that your dog should be fine!!
Let me explain...
There are a number of different rodenticides (rat or mouse poisons) available. The most common ones act by preventing the body from forming clotting factors which allow the blood to clot.
The body has a store of clotting factors, but no new clotting factors can be made if the animal eats this type of rodenticide. Thus, symptoms do not start immediately, but instead start days to weeks later (depending on the amount of poison eaten).
This is true for the mouse/rat too - it does not die immediately that it eats the poison, but instead dies some days later. Thus, it is very unlikely that the mouse actually had any poison in it on the day it died! Thus, very unlikely that your dog ingested any poison, or if there was some it would be a tiny amount.
When a dog or cat eats a poisoned mouse and is thereby poisoned, it is called "relay poisoning" and it generally happens when the dog/cat catches a LIVE mouse that has poison in its stomach and intestines. And a dog the size of yours would have to eat several live, poisoned mice!
Just so you know, when a dog eats a rodenticide, they will produce a green or blue stool about 1 day later, and start showing symptoms of illness 1-4 days after that. Rodenticides typically cause internal bleeding, which can cause lethargy, vomiting and inappetance, and finally death.
Rat poison is made to taste good so that the rodents will eat it - unfortunately, it tastes good to dogs too and they will also eat it if they find it. Most of the bleeding will be internal (into the belly and lungs) but sometimes we will see blood in the urine, stool or as a nosebleed. So, I do have some concerns about having rat poison on the property at all... but that is a separate issue!
The good news is that there is an antidote for rodenticide poisoning, if you dog does get into the actual poison! Vitamin K1 (and ONLY vitamin K1, not other forms of vitamin K) given by mouth will act as an antidote. The dog needs to stay on them for weeks to months, and they may be expensive. There is now a much more affordable chewable 25mg and 50mg tablet available in the USA.
Here is more information about rodenticide poisoning:
So, your dog should be fine, but do be VERY careful that she does not find the mouse/rat poison as she will be able to smell it and will seek it out as it tastes good!
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The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would strongly advise contacting your regular veterinarian.
Best wishes to you and to your dog!