You can't have ONE rabbit living outside - s/he would be miserable.
Your three year old will be bored within a week, and your rabbit will be bored of your dd long before them.
Rabbits are not good pets for children. They are a prey animal, they have totally different instincts. Unlike a dog, they are not remotely interested in pleasing you, their sole focus is usually where the next tasty treat is coming from! They are absolutely beautiful, fun to watch with each other. They hate being picked up, at the best they might like nose rubs.
I had three, the dts got bored very quickly and they became my rabbits, I loved them. I didn't care that they hated being picked up - they had the run of the garden, and would charge down as soon as I opened the door to see what food I had for them! They ate pretty much everything in the garden - my veg patch, the roses, the evergreen bushes, the lawn down to it's roots. They dug a big burrow at the back of the garden. I loved seeing them do normal, rabbity things. They were not for cuddling.
They are expensive. Insurance £6-7 a rabbit, vet plan was around £6 a rabbit to cover vaccinations, check ups, worming. Feed on top of that - £11 for a big sack of pellets, about £6 on hay a week for my trio. Neutering I think is around £60 ish. If a rabbit gets ill (which can happen very quickly) you can be looking of bills of hundreds. Boarding fees are about £9 a day for two rabbits for when you are away.
Cleaning up never bothered me that much, they can be trained to use a litter tray lined with newspaper and filled with hay. The smell isn't half as bad as that of a dog or cat. You will get mice, and slugs galore in winter, and traps or poison can be hard with rabbits bouncing around.
They need a large hutch - ideally a 6 footer, tall enough to periscope, and then access to a large run. Free ranging should only be done with supervision.
Sadly I lost two of mine to a fox, after one of the children left the hutch unlocked at night (I should have checked). I had to rehome the third as it would have been cruel to keep her alone. After having them and realising how much work it was, I really didn't want to take on, and fall in love with more rabbits.