I am very sorry to hear about your girl.
I hope your remaining hen is not too lonely or that you can find a friend for her.
We had to modify our dogs yard last year because the chickens and guineas kept going in there. The dogs would then play with them and hurt them (they mauled one of my guineas severely and he lived). When a dog bite punctures the skin you have to be very careful.
Sorry I didn't find this sooner, but for future reference...
From LSU on dog and cat saliva:
"Over 130 disease-causing microbes have been isolated from dog and cat bite wounds.1 Animals saliva is also heavily contaminated with bacteria, so a bite may not even be necessary to cause infection; if you have a cut or scratch and allow a pet to lick it, you could be setting yourself up for trouble."
For any animal bite on your birds:
Thoroughly rinse the wound with water and then carefully wash with soap and water.
Follow this with an antiseptic such as iodine and then apply an antibiotic cream such as Neosporin.
If it is possible to bandage do so...if not then you could then spray with liquid bandage or wound kote.
Then isolate the bird to a hospital cage. If it is excessively hot or cold outside it may help to bring them inside to reduce stress from the heat.
I also offer some electrolytes in their water for at least the first 24 hours.
If you have an antibiotic such as Tylan or Oxytetracycline on hand, you could dose them with that too...just to be sure.
This will not always save the bird, but it has worked for me on even my most severe cases.
Good luck in the future.