Maybe a rabbit. They dont take much space and are quiet. To tie into the permaculture part, you would be able to show your daughter how the poop can help grow stuff which you can then feed to both the family and the rabbit. In the garden, set up a toad house for fun and teach pest control if she likes less furry critters too.
I was going to recommend a rabbit, also. Rabbits enjoy eating fruit tree and rose prunings. It's important to the rabbit's health that it chew on wood, so you teach her about animal care and pruning at the same time.
In personality I've always found them to be most like cats, though they take better to a leash. You can train them to use a litter box so they can run around rooms with hard floors. The hard little pellets are uncontrollable but on a hard floor you just sweep them up, it's one of the great things about rabbit droppings. The other one is that they can go directly on the garden without worrying about smell, disease, or burning the plants.
The real key to this working is taking time and attention to socialize the rabbit. Especially as this is her first time with a rabbit, take the time to find the calmest rabbit you can. Talk to the rabbit and handfeed it treats. Those rose and fruit tree prunings are great, too many carrots are like too much cake for a kid.
In dietary needs, get lots of real hay. That should be the bulk of the diet. They need all that fiber to keep their digestive system flowing smoothly. That could easily be the most common way pet rabbits die is people feeding them too many rich foods (vegetables, pellets, and treats) without enough roughage. The wood and hey also keeps their teeth in good condition so you won't end up with a dentist visit for a pet.
I know, you haven't decided on a pet yet. I just think it can help the decision process to have enough information while you think.
My much better half and I got a Flemish Giant rabbit in February, and my compost hasn't been the same since. It's amazing.
We were trying to decide between a specific breed of cat (allergies) or a rabbit. What decided me was the waste. Cat waste is hazmat suit worthy. Bunny poop can go right on the soil, though I compost, for the paper bedding she uses.
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein
Another vote for bunnies!
We have two, indoor bunnies.
They get pear and apple tree prunings, select "weeds" and the stalks of jchokes.
We get perfect fertilizer and bunny cuddles.
The thing about rabbits, they might love the petting , but most hate being picked up.
They are kinda fussy, and flirty, and can turn on you in a second,kinda like a vegetarian cat.
I find that the feed back loop with kids is amazing and posistive.
This board helped me decide on a rabbit for my little girl, about 3 years ago.
I would love to have more, mostly for poop, but if i do, they will live outside in a shade house, and eat way more things than the pets eat.
I'd suggest that you get a couple of chickens! They have tremendous personality, are relatively low maintenance once they are about 3 months old. They'll clean up your food scraps and provide eggs.
Bunnies are soft and cuddly when they are small, but as they grow, they can get aggressive and might even bite. Yes, had it happen to me once and it took a chunk out of my finger. Chickens are hardly cuddly, but as they get older, they are more willing to be held and petted.
We keep our birds in a 4' x 8' chicken tractor --- 8 birds. I'll open the door and let them run free for an hour or two at night so they can run and flap and express their chicken-ness. Some days I'll leave them out much longer if I'm out there in the orchard working. So even though your space is limited, you could easily build a coop that would hold 3 or 4 birds -- enough for eggs for the family.
Of all the breeds we've raised over the years, my favorites are Plymouth Bar Rocks. I also like Rhode Island Reds -- either of those breed have great personalities, are great layers, and when their egg production slows down (after their 3rd summer), they are a nice meat bird (albeit, they are pretty tough by that time).
"The rule of no realm is mine. But all worthy things that are in peril as the world now stands, these are my care. And for my part, I shall not wholly fail in my task if anything that passes through this night can still grow fairer or bear fruit and flower again in days to come. For I too am a steward. Did you not know?" Gandolf
We had one chicken with our 14+ ducks, and MAN did that chicken do damage to the garden when she managed to get in. Ducks are easy to keep out of a garden, and, as I like to say 10 ducks will do less damage in an hour than one chicken will do in 10 minutes. Our chicken got into my son's garden for less than 30 minutes, and pretty much destroyed the whole garden scratching and pecking. I think with a small plot like you have, Branko, two chickens in a coup would be fine, better if you have lots of scraps to feed them and/or have them in a "tractor"-style coop that you can move around so they have new areas to destroy--I mean till!--for you.
Our neighbors have to chicken in a tiny coop and run. It's 2 foot by 6 foot, if that. They don't get scraps or get moved around or let out. But, somehow, they still look remarkably healthy. I'm sad that they are in a small space, but it doesn't seem to bother them. It would drive my ducks nuts! So, while a small coop is not ideal, I think there's ways to make it work if all you have is a small plot.