Gail, I love pugs!!! I grew-up with a pug, and then I got my own as a puppy, Jaeger, who died about 3 years ago now at 14...I still miss that little ball of wrinkles and snorts.
I grew-up with dogs and birds (a lot more birds than dogs since my mom was a breeder, then so was I), and I currently have a male Shar Pei who is 2, and an Australian Cattle Dog who is 4. And never in my 38 years have any of my dogs liked the birds at all. However, there has been a very distinct difference in how the dogs have reacted to certain birds. It's amazing how insightful and jealous they can be.
I grew-up with a "pet" Congo African Gray, an American Budgie, and 2 Cockatiels, and then we had dozens of breeder-birds, both American and English Budgies, BeBe Parakeets, Linnie's, Princess of Wales Parakeets, Cockatiels, and different Conures. And now I have 8 Budgies, a Ringneck Dove, and 4 larger parrots who are all "pets", and then 5 remaining breeder's. And throughout my entire life not one of the dogs ever became even remotely "friendly" with any of the birds. And like Gail said, I'm happy that they haven't, because the minute you let your guard down even a tiny bit, that's when tragedies happen.
However, as far as the breeder-birds go, the dogs have all pretty much totally ignored them and not even acknowledged that they're in the house. My indoor-aviary is right next to my work-out room and my wood-stove, so my dogs are always down there when I'm down there, and they actually lay in front of the aviary and sleep, but they never even look at the birds. And that's how it always was growing up too, the dogs weren't even interested in getting into the breeder's room or the nursery at all. Just not a factor to them at all...
That being said, lol, my dogs show active jealousy towards all of my pet birds on a daily basis, and they did growing up as well. My 2 current dogs have never once growled at, barked at, snapped at, or shown any bit of aggression towards any of my "pet" birds, but they do both show outward signs of jealousy and actually competition towards all of them, especially my Cattle Dog (Heeler's are extremely loyal, 1-person or "family" dogs who fiercely love their owners, almost too much sometimes). I always have at least one of my birds on me somewhere, lol, the 4 larger parrots and the Ringneck Dove are all fully-flighted and free in the house whenever I'm at home (the 8 Budgies get their own block of time free in the house or in a separate room with a latched door). And both of my dogs are constantly whining, crying, and barking at me, not the birds, whenever any of the birds are interacting with me. And my Cattle Dog has a real issue, ANY TIME she sees me petting, holding, cuddling, or even just talking to one of the birds, she whines and rolls around on her back with her feet in the air, making cute little noises, trying to get my attention. I could have just spent hours with her playing in the backyard, on a hike, on a ride in the car, etc., doesn't matter, the second we walk inside the house and one of the birds flies to me, the whining starts and she's on her back in her "begging" pose, like "Wait a minute, I thought you loved me? Stop touching that bird!" She can be totally entertaining herself with a toy or a ball, or really be into chewing a new pig ear or a bone, doesn't matter, the second one of the birds flies to me or I go and pick them up she becomes insanely jealous and starts "begging" for attention. And that's pretty much been my experience with my dogs and my birds. Luckily I've not ever had an accident/attack/injury involving the dogs and the birds, but I still would never risk having them alone together unsupervised for even a second. They all know our "routines" when we're inside the house together, where they need to be and when, etc. regarding the birds. But they're still natural predators, and you always have to keep that in the front of your mind...
I know that there are people who seemingly have a household with birds and then another "predator" pet, or pets, such as dogs, cats, ferrets, etc., where they say that their birds and their other predatory pets "love each other" and "are best friends", and they usually post photos of the dogs or cats laying there with the birds sitting on their heads, or them all laying together on the bed cuddling or playing, and I don't ever mean to offend these people because they really do seem to get along together well and seemingly "love" each other...I see this in my Bearded Dragon forums too, people who swear that their cats (it's always their cat) love their Dragons and that they are "siblings and friends", and they post photos of their cat laying on the floor with their Beardie curled-up beside the cat or on the cat...and I cringe and hold my breath, because I cannot tell you how many cat attacks on Bearded Dragons I've seen on the forums, it literally has to be over 100...and it always happens "suddenly" and "out of nowhere", and they have always "really loved each other", etc. And unfortunately in probably 95% or more of these incidents that Bearded Dragon dies a horribly slow and agonizing death due to the cat either biting down on their head and causing brain injuries, or the cat has grabbed the Dragon in it's mouth and shaken it/batted it around with it's feet/claws, and caused internal injuries and bleeding. And the owners are always absolutely shocked that it happened, because their cats "just aren't like that"...
Bottom-line is that cats, dogs, ferret and other rodents, some reptiles, etc. are all predators and the birds are always the prey. And all cats are natural hunters, even the most docile, fat, lazy, loving house-cat that has never gone outside and never chased or bitten anyone or anything. So the idea of your bird(s) and your other predatory pet(s), whether they be a dog, a cat, a rodent, a large reptile, etc., doesn't matter, being "friends" or becoming "friendly with each other" is not typically reality, it's just not how nature works. Yes, there will be situations where a dog seems to "like" a bird, or is "friends" with a bird that it lives with, I've seen it and cannot deny it...However, I still cringe and hold my breath...