The use case will dominate a choice of device.
The iPad became so popular because it didn’t try to be a general purpose computer. It was the idea that tablet computers should run a standard desktop OS and tools that doomed Microsoft’s initial forays. Apple made the connection that most people don’t want or need productivity applications on a personal device. They also realised that there was an opportunity to address a large fraction of the populace that was not comfortable managing their PC. Apple are derided for the walled garden approach, usually accused of creating it with the desire to totally control the flow of money to their benefit. There is some truth to the claim, but it misses the crucial thing. 99% of users are not geeks, and don’t want to be concerned with the geeky issues that come with a more open platform. Apple lock down the platform so hard that it is actually hard to get into any sort of trouble. Time will tell how much they will need to open things up as the competition (mostly Android, but including Windows, and maybe RIM and other minor players) adds more freedom.
The thing about an iPad is to not confuse it for a computer. It is a computer in the same sense a smart TV is a computer, or your phone is a computer. It has a computer in it, but it isn’t a general purpose computing platform like a PC. It is a personal consumer device that provides a set of functions - like web browsing, video calls, music, photo library, a simple camera (people taking photos with their iPad look idiotic, but it works) and for the yoof (and not so yoof) of today, games. Don’t forget games.
You can make an iPad into a limited personal productivity device - you can get apps that provide word processing, spreadsheet, presentations, and get a keyboard for it. But it isn’t very popular use for the platform.
An iPad is the defualt device for a tablet in much the same way that Windows became the default operating system and the Windows PC, the default personal computer. It is popular, it is the best supported platform, most other people you interact with will have one. And so on. Apple devices have a couple of hidden advantages. Apple are pretty good at supporting their products as they release new software. Eventually the new versions of the operating system will make demands on the hardware that older devices just can’t manage, but until then your iDevice will be fully supported with new operating system releases. Android vendors have had a terrible reputation for abandoning their products with no support or updates. They are getting better now, but it wasn’t good, and significantly annoyed a lot of people. Also, iDevices have a very good second hand value. There is probably no good reason for this (apart from the good support Apple provide) but the reality is there.
For the use case described, and especially if the goddaughter has her heart set on one, it is easily the right choice. There are a range of versions. Two sizes, a range of memory, the big ones have two different screen resolutions, and optional cellular data connection. I rather like the mini, but that is just me.