No, do not use Hydrogen Peroxide to clean out wounds on your bird, for a lot of different reasons, one being that it's not very effective, and the other being that it emits fumes that could be toxic to your bird...Hydrogen Peroxide does not do a good job of killing bacteria/fungi anyway, but it's just not a safe disinfectant to use on a bird.
You should have a "Bird First-Aid Kit" in your house with all of the things that you need in any emergencies like this with your bird. As far as what to use to clean-out the wound on your bird's foot (to prevent infection, that's going to be the main issue with the bacteria in a dog's mouth), you want to use either Hibiclens or Betadine. Both of these are available at any grocery store, drug store, or Walmart, and they are right in the aisle with the rubbing alcohol, peroxide, Bactine, Neosporin, etc. Hibiclens is best, as once you use it to cleanse the wound, you don't rinse it off of the wound but rather just let it dry quickly, and it forms a protective barrier from bacteria and fungi from getting into the wound for up to 24 hours. A bottle of Hibiclens costs about $5 at Walmart. Betadine is also a good choice, it's Povidine Iodine, and with it you need to dilute a little of it in warm water until it looks like weak tea, then use it to cleanse the wound, ad let it dry. Again, it costs around $5 a bottle at Walmart, and it kills most bacteria and fungi. And neither Betadine or Hibiclens emit harmful fumes that will hurt your bird.
***Just for future reference, try to get a First-Aid Kit together that is only for your bird, and put it in a place in your house where you'll always know exactly where it is, so if there is an emergency, such as a broken blood-feather where your bird can bleed to death quickly if you don't get it stopped, you'll be able to just grab the First-Aid Kit and go...The vital things you need to have in a Bird First-Aid Kit are:
-Corn Starch for stopping bleeding from the skin or a broken blood-feather (corn-starch does not burn or cause pain to your bird, so you should use it on any bleeding coming from wounds on the skin, and is a must for a broken blood-feather, as you need to just dump it on the broken feather shaft)
-Qwik-Stop (powder is better than liquid) to stop bleeding of broken toenails, or if the corn-starch isn't able to stop the bleeding from a blood-feather that has broken
-Betadine and/or Hibiclens
-Triple Antibiotic Cream such as Neosporin or Bacitracin
- it's used on a lot of wounds (including burns) because it's kind of antiseptic.
