Oh, I love Dals! Great dogs!
Ok, so the short answer is that it should not be a problem for the dog to stay in the house.
However, the longer answer is that you should take some precautions for about 3 weeks after the I-131 treatment.
I would have your husband avoid prolonged contact with the pup. So, no sleeping on the bed, and no sitting on his lap on the couch for more than about 5 minutes.
It is good that the pup does not drink from the toilet, as he could otherwise be exposed to I-131 that your husband will pass in his urine. To be extra safe, keep the toilet seat closed!
Your husband will have I-131 in his bodily fluids for several weeks after the treatment. So, things like feeding the pup from his mouth should be avoided (this is something that my trainer tries to get me to do with our dog - taking a piece of cheese out of my mouth and dropping it into the dog's mouth to encourage "look at me" behaviour).
I do not anticipate any problems with your pup staying in the house. However, I will just mention that your Dal *could* develop hypothyroidism as he gets older, completely unrelated to your husband's I-131 treatment.
Hypothyroidism is a common problem in many dogs as they age. With this condition, the thyroid gland stops producing adequate quantities of a hormone called thyroxine or T4.
As I am sure you know, T4 controls metabolic rate - the more you have of it the faster your metabolism.
So, in dogs that are hypothyroid, there is not enough T4 and they have very slow metabolisms. They tend to put on weight easily, and sleep a lot, especially in warm spots like in front of the fire. They may develop poor hair coats and be prone to infections (skin, bladder, eye, ear and other). It is diagnosed by a blood test and treated by giving a thyroid supplement. It is not "cured" so supplements must continue for the rest of the dog's life.
I hope that this helps, and that your husband's treatment goes smoothly!
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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.