The same thing happened to Owen. We were home, Owen was outside and got stung by a spider. He had a very severe allergic reaction to this bite and had to be rushed to the vet. If we weren't there he would have died.Loke said:Loke was stung and had a reaction while I let her out while I was home, if I hadn't been here she would have died.
You can take all the precautions possible and puppy proof everything you can think of but there is no way to avoid something like this happening.
What about leaving him in the kitchen or getting a dog sitter?