Guinea Pigs are friendlier. We had quite a few when we were little, which eventually became my Mums, as all animals eventually do with small children. There is quite a lot of work involved, and your back lawn will become kinda gross looking as the cage is moved around.

Oh, and if cats or dogs come inside, check down the sides of the couch regularly before leaving a bigger animal inside  (some of ours got eaten because we'd let them run behind the cushions on the couch and forget about them).

One house we rented came with a free range pet rabbit. Our first encounter with the neighbour (rabbit's owner) was to see him running full tilt across our lawn with a giant net on a pole! We didn't know the rabbit lived under our house at that point and wondered what on earth he was doing lol . It was a cute bunny, but rather shy, and fought madly whenever captured.

I'm not a cat fan personally (no offence anyone), so thought I'd throw another couple of ideas in the mix.

We bought four hens a couple of months ago - they free range in our garden and get locked up in their coop overnight so cats/stoats don't eat them. They do poo everywhere, but our garden is over an acre in size and it rains heaps here . Oh and they will attack the vege garden too, so that needs to be fenced off. But Jimmy adores them and spends hours each day chasing and trying to pat them, or watching them out the window if he's inside. Today I let him bring an egg from the nest, all the way inside (long way for a toddler) and he was so excited. They're pretty easy care pets, but it helps if you have a biggish back yard.

I had pet lambs as a kid, from a young age, and we want Jimmy to have them too. They are very gentle animals and hugely rewarding. Often farmers are happy to "loan" a motherless lamb out to people until weaning time (a few months later) when they'll take them back. They can live in an average sized backyard that is well fenced, with no poisonous plants, and really only need a dog kennel type-thing for shelter. I used to mix up the milk for the lambs bottles and do all the feeds myself from about Keira's age - under supervision of course. Kids (as in baby goats) are heaps of fun too, but probably more suited to older children, and are much better escape artists than lambs!

You'd have to check Council rules though as to whether you can have pet lambs or chooks in town.