I haven't used a Nabi, but while the tablet's design may be more kid friendly, I can't help but think that the content available will be sorely lacking in comparison to an iPad.
If you're wondering whether your kid may be too young for an iPad mini, I don't see how the age factor would be any different here. It's still a $200 device that's still perfectly capable of breaking. If it was my child, I'd get them a mini and take advantage of all the kid-friendly iOS content, but you may feel more comfortable spending $199 than $329 on a young child, and I can certainly align with that, especially if money is an issue for you like it is for many people at this time.
If you don't want to spend more than $200, I would probably be more inclined to look at the Kindle Fire HD, something closer to a true tablet whilst still retaining kid elements.