Offer to pay for the blood work and anything extra that the shelter doesn't typically cover. If your vet thinks she has a URI and can exempt her for a week of abx, that could help. I would ask for that, though I have seen sick dogs go through speuters (HW+, undiagnosed respiratory issues) okay, I would want to delay it until that cleared, especially since it's been ongoing for 4 days and is not clearing.
It could also be a symptom of roundworm. Why Is My Dog Or Cat Coughing?
I would want to wait until a week after a de-wormer is done.
So bottom line for me is can my vet get me that extra week so that I can get her in a better place for the surgery.
You are in the south and shelters are now really trying to stop the people adopting to breed cycle (or adopting and then dogs breed by oopsie). There are so many things you can, and will do, to impact her health in a positive way (weight is a huge one - good nutrition, exercise) and her genetics will play a huge part in her overall health anyway, and how her body reacts. http://www.columbusdogconnection.com/PedSpayNeuter.htm
has some information for what you will probably be hearing.
I have a 9 yo next month female 50# mix from NC spayed at 8 weeks. She has bad hips, had one FHO which was curative for that hip, and the other is maintained well with supplements - since she was not xrayed at spay, I don't know what her hips were like before I had her checked. She had one URI once. Knock wood - she's had almost 9 great years so that to me is a success. I have an 8 yo male 65# mix from SC who was neutered probably at 5 weeks. Yeah - that's earrrrrly. There were complications with the anesthesia - have to be honest - we tried to get the puppies without them doing the surgeries then, but that was their policy - he has some issues/delays but 5 weeks is hugely different than 8 even. He goes to the vet 1x a year again, knock wood! The rescue I volunteer with now goes for 14 weeks. They come out of their speuters ready to play.
I'd also ask them to do a bleeding time test. They are like $10 at my vet office and while not perfect, give me a tiny piece of mind with breeds that are bleeders. https://ahdc.vet.cornell.edu/clinpat...coags/bmbt.htm
eta - re - spay incontinence -