These things happen, and you're right, they almost always do happen in a "split-second", and before you know it it's already happened. Christa had a good suggestion of totally separating the dogs and the bird, as there is such a size difference between the two, and since you never know how they are going to react it's just the safest thing to do. I have medium size dogs that have never even shown interest in any of my birds, but I still refuse to even allow the birds to be anywhere near them, even when I'm in the room, because there's nothing that I'm going to be able to do because as you found out, it just happens in the blink of an eye....But don't beat yourself up, it was an accident, live and learn from it, that's what's important.
***As far as your Green Cheek goes, he's most-likely in a lot of pain combined with just the shock/trauma of the whole thing. Keep in-mind that he's most-likely going to be very afraid of that dog from now-on, so for his psychological health (in addition to his physical health) I'd make sure that he cannot see the dog at all for the time-being. Birds can become extremely stressed-out very quickly over things like this, and even though it happened a full day ago, seeing the dog could stress him out again quite a bit, and stress and birds don't go well together, they can actually have a lot of health issues result from stress like that...
***As for his foot, make sure that you are keeping the wound clean and disinfected with something like Betadine or Hibiclens, as the biggest thing right now is preventing an infection arising from the bacteria in the dog's mouth, or any other bacterial getting into the wound. As long as the wound isn't exposing any bone and is only superficial, then you just need to disinfect it several times a day and then pat it dry. You can also put a dab of either Bacitracin or Triple-Antibiotic Cream (Neosporin or generic) on it twice a day, each time after you disinfect it.
***Take not if he's still having trouble climbing, perching, etc., or if he's still favoring that foot when he walks or when he's standing as of tomorrow morning before you go to the Avian Vet, and let them know, because it's quite possible that he might have a fracture of the bone in his toe; they are such tiny bones that it doesn't take much to break one. This is another reason you absolutely want to disinfect the open wound a couple of times a day and put an antibiotic cream on it afterwards each time, because anytime that you have a fracture of a bone and then an open-wound near the fracture, even if the wound is superficial and not exposing the bone, because bone is so vascularized and has such great blood-supply, any bacteria, fungi, etc. that gets inside of even a superficial wound that is near/above/below a fractured bone, there's a very good chance of that bacteria spreading right into the open bone of the fracture through that very dense blood supply. Even though these kinds of fractures are not consider to be "compound" fractures since the bone is not exposed to the air, they are still considered "open" fractures because their is a superficial wound right above/below/next to an underlying fracture, and this greatly enhances the chance of a bone/systemic infection. So just be sure to keep disinfecting that wound several times a day.
Hopefully it's not fractured, but if he's still favoring it tomorrow and if it is still showing any redness, swelling, etc., the Avian Vet should do a quick plain-film x-ray just to see what the damage is, and to see if a splint or some type of immobilization is going to be necessary for it to heal properly. There isn't a whole lot you can do for a broken toe in such a small bird, but you do need to know what the risk of a deep infection is. They should also give him at least a prescription anti-inflammatory, like Metacam, and possibly also a prescription pain medication, like Tramadol, and also an oral or by-injection antibiotic... It just depends on whether it's fractured or not...he'll most-definitely get some Metacam and an antibiotic...
Keep him quiet, warm, and stress-free until the appointment tomorrow. He'll be fine, you just want to make sure that he's suffering the least amount of stress as possible. And again, don't beat yourself up, these things happen and it wasn't your fault. Just learn from this mistake and make sure that it can't happen again.
So sorry this has happened. 
