I've had a Blue-fronted Amazon parrot, American and English Budgerigars, Cockatiels, Canaries, and several breeds of Chickens, Ducks, Geese - they all have their special uniqueness and I think they trained us instead of the other way around! I think it's sweet you're willing to have a house chicken. Keep in mind that most birds are "flock" animals and one chicken alone is not the norm. Your DD may have to entertain having 2 in-house chickens for their "flock" mentality if they are not going to be integrated into an outdoor group. There is nothing cuter than 2 bantam Silkies or 2 bantam Cochins or 2 OEG's toodling around the house (or the backyard!). Of course, if 2 house birds are out of the question, the mirror is a second option. We had a lone Dom chick that visited her blankie and mirror in her cage whenever she wasn't following us around the house. It wasn't the same as a 2nd chick but we had to think of something so she wouldn't feel isolated. House dogs and cats need to be monitored. I would not consider leaving them alone with birds no matter how well-behaved they are when under supervision. I've heard too many sad stories of losses from "friendly" pets.
Due to pack mentality, we only allow 1 dog to be lose in the house and the others are crated when we are gone. We have 3 indoor cats. I am 99% sure they could hold their own, as my big male is 26lbs (yes, he's obese, and he's been on a diet for years, the smart ****** will go eat dog food, get into trash, and learned to open any door, cabinet and lock that wasn't with a key, to find food. He'll even eat grain and chicken feed if he feels were starving him - he's a work in progess, but now that he's in double digit years, I've sort of resigned myself to his heftiness- the vet said he wasn't even as fat as I thought he was... so as long as he's not showing overt strain, he's okay.)
Anyways - The chickens would be in her room, and I'd probably let them out if only the cats where inside, and they were full grown I don't see any of my cats messing with a full grown chicken. (none of our outdoor/barn cats messed with the chickens, and our indoor cats are used to raising baby humans, goats, and other things. I think if anything, the chickens are more likely to terrioze them since 2 out of the 3 are skittish, and my big one doesn't do much but lay there.)
Our 3 legged pitbull is the only one who gets free range of the house - and it's because she's got 3 legs, and doesn't cause any trouble. My bulldog and boston terrier are nightmares when it comes to chewing anything they can get their hands on (so they have LOTS of bones in their kennels.) and my daughters rescue dog, is one of those "Excited peers" and has never out grown it....
Our bulldog, and pitbull are the only ones really allowed any freedom - but our bulldog only gets it if we are there to supervise. My boston's an insane dog, who is stupid as a rock. I probably could train him up a lot better than he is, but he's a good natured dog who doesn't cause any problems besides stealing socks.... or shoes, or anything you remotely set down for a split second... he takes. LOL I'd love to see a chicken terrorize him.. (okay, not really... but the mental image was funny.
I wouldn't trust them lose in the house unsupervised. We use baby gates and other stuff to help confine even our dog whos free in the house and not kenneled, she has a dog bed, and wiht our toddlers, I don't want them being able to grab cats, or dogs randomly either. It really feels like our haze is a maze of gates some days. LOL
ANyways - long ramble short.
Chicken would be only free in her room to hang out with her - or if all the dogs were outside, or kenneled and we did a careful introduction with the pitbull. She's not a fan of being harassed due to only having 3 legs, so I don't see her messing with a chicken if the chicken ignored her.