I don’t usually draw the blood myself on my own pets- though I usually do hold them. I held Griffin wrapped in a towel and the vet drew the blood from the huge vein at the base of his ear.
The volume of blood that you can draw from a rabbit is based on weight- so waiting for a smaller rabbit to get larger can be of benefit. Working on smaller pets is more delicate as they have smaller veins, etc- so if Griffin was a small rabbit I would wait until he was 5-6 months old- just so he is bigger and stronger.
Some vets have preference on when they will do the surgery- my vet does not like to spay before 6 months old- and usually neuters around that time- but since I know Griffin’s age and that he is strong and healthy- she is OK with neutering earlier (though not spaying earlier).
Young cats and dogs CAN be spayed as young as 8 weeks old at a Humane Society or shelter- but most regular vets wait until 4-6 months before agreeing to surgery. The shelters goal is to have none of their pets add to pet overpopulation- the vets goal is to have a successful surgery on a healthy patient.