Both my girls came home the same day. They both did fine.
Both of mine were older than 6 months old. I think the blood test depends on the vet. I would ask my vet about it. Rosie was 8 months old I think when she was fixed. She had not come into heat at that point. A friend of mine got a female at 8 months old and she came in a little over a year old. I think it may depend on the dog but I really have no idea. If it was me, I would wait until after the shot or at least make an appointment to discuss your concerns with your vet.