Hi Ed. To be honest, gerbils are great, but at 3 years of age, your daughter is still very young and gerbils can be (a) fast and jumpy and (b) don`t like being held and can (and will!) bite.
It`s tricky with rodents for children this young because although the adult in the house will be doing the cleaning/feeding etc....the gerbils ( moreso females) can be known to fall out and de-clan, although males can also de-clan even after living together for a few years. I`ve had this happen a few times in the past. This means having another tank set up for the one that ends up ousted by it`s cagemate.
Do you have any other pets at the moment or were you just looking at something to have that your daughter could enjoy watching? I wouldn`t go down the barred cage route for gerbils in any shape or form because they chew the bars and can injure their teeth. Far better with a large enough glass tank that`s at least 3 feet in length with a secured meshed heavy lid. Gerbils are diggers, not climbers.
You mentioned Snails? These actually DO make good interesting pets that don`t bite and are very easy to care for and keep. Plenty of info on the internet about them too. Garden snails (the ones with the shells) can even be re-released again into the garden in early summer if your daughter got bored, but you can`t do this with African land snails or foreign species, for obvious reasons!