I've had birds all my life. I love them and have found them to be great companions.
My son was born into a house with birds. So, he was very used to them.
They were parakeets. We had two. One was far more friendly than the other. Pepper really didn't care for being held or sitting on your shoulder or anything. I had a big standing cage on a base with lots of toys and things for the birds to climb around on.
Parakeets will bite if they feel threatened and Pepper wasn't afraid to nip, even when I was just cleaning the cage.
My son was 2-1/2 and potty trained so one day when he went in the bathroom I didn't pay much attention, but he had carried his stool that he used for getting on the toilet, to the bird cage. He was being awfully quiet so I went to see what he was up to and dang if he didn't have his little hand in that cage with Pepper sitting on his finger. Neither one of them had made a single sound and I could not believe my eyes.
They were pals from that day forward.
The bird that never let anyone mess with him sat on my son's shoulder, on his head. I have pictures of my little guy laying on his tummy in his super hero underpants watching TV with that bird on him. You might think the bird would take off and fly away the first chance he got, but he didn't. And he never bit my son. The bird would screech his head off when anyone else tried to hold him and you wouldn't believe it if you hadn't witnessed it. But, I do have witnesses and pictures.
My son was so little, in fact, that he didn't say "Pepper", he said "Pecker".
And, we did get some funny looks when he told people about holding his Pecker.
When Pepper passed away, my sister bought my son another bird for his birthday. He named her Sparky. He finger trained that bird. He was so patient and knew the difference between a nip and a bite.
Birds really can bite hard. They can break the skin. But, it's a matter of building their trust. We are WAY bigger than birds and we can hurt them much more than they can hurt us.
Sparky lived a long time. She got a tumor on her wing and this might sound crazy, but I paid $150 to take her to a bird specialist who did surgery on a $15 parakeet. That bird slept with me, in my bed, under my shirt, while she recovered. She did great for a couple of years, but developed another tumor that wasn't operable. My son stayed in my bed with me and he was holding her when she passed away very early one morning.
We loved birds so much that my sister bought one for my nephew but he never had the patience for it. And he didn't like the chirping. He was like a bull in a china shop so the bird bit him even though my son was able to handle it. They gave the bird to my son after Sparky passed away.
My son renamed her Paloma and we still have her. She's 8 years old. I've had birds who've lived quite a long time. My Sunny was 15 when she passed away. She never talked, but she mimicked my whistling every morning and when I came home from being gone.
Birds really can make good pets. You need to keep their cages clean. Always make sure they have water and treats. I buy bird food and treats at the feed store. Some also enjoy a little lettuce or fruits to munch on.
You can buy really good books about parakeets and teach your daughter to be gentle.
Like I said, I've always had birds so it seems natural to have them. But keep in mind that they will bite. My son has trained other people's birds by putting a sock on his hand so if they get scared, it won't hurt him and they can bite without retaliation or yanking away. Once they know you aren't going to hurt them, even if they bite, it builds their trust.
I should have my son telling you all of this. He's even better with birds than I am.
They are a committment though. If you don't want a bird chirping in the morning when they hear the other birds wake up and get going, it might not be the best pet for you. I, personally, don't like not having a bird in the house. But, my grandfather always had birds, I've always had birds, my son will no doubt always have them.
He was in the 4th grade and wanted to take his bird for show and tell. His teacher was very much against it because she didn't like the idea of something being caged. My birds have "travel" cages even, and the teacher relented. My son brought the bird out for his classmates and talked about how to care for them. The teacher said she completely changed her mind about having a bird for a pet. It was obvious there was mutual affection.
So, this got super long, sorry, but you might want to get a book first before buying a bird. I don't think they are all that difficult to take care of. You want to make sure you have a nice big cage so they can flit around. If you let the bird out, you have to make sure it can never get outside because the poor little things can't survive on their own. I know plenty of people who love bigger birds, like parrots, but in my opinion, they are very messy and require a lot more focus and attention.
I don't think a bird is a bad pet as long as you know that you will be the one doing the care. Your daughter is too young to be responsible for that, but she can learn. And, they are much easier than having a cat box or a dog that needs to be able to run and poops in the yard, etc. Allergies could be an issue with any pet, but my kids never had any problems with birds.
I love birds so I am biased. They do have personalities. They love music and the sound of running water. Some like baths, some don't. Some are affectionate, some are timid. Obviously, being so small, they aren't like a cat that a yank on the tail won't harm them too much physically. I'd rather have a bird than a hamster anyday.
Another thing is that if you travel or go out of town, you just need to make sure there is plenty of food and water and birds will be just fine by themselves. They go to sleep when it gets dark and they wake up with the sun and the sounds of other birds.
I wish you the very best!