Aw, bless her, I remember being the same when I was a nipper and now I'm a right fish geek 
Bowl shaped tanks are no good at all for fish. They don't have enough surface area for proper gas exchange, they are a bugger to clean and they don't hold enough water. I've never seen one big enough for goldfish, which get very large and very messy. A bow-fronted or corner tank would be much better if you don't want to go with a traditional rectangular one. Steer clear of the death bowls though!
Goldfish are lovely fish but most people can't or don't want to provide them with the right environment. They get massive, they need a lot of cleaning and they live for years (plan for 20!) so they are not a cheap or low-maintenance pet. They are very rewarding though, especially if your DD is into science.
The best way to start with fishkeeping is to see how much space you have for a tank. I wouldn't keep any fish in less than 45 litres (depsite the numerous beginner and lifestyle tanks available that are much smaller than that) and 60 litres would be a good starting point. If you want to go for goldfish then you'd need at least 150 litres for a pair of fancy goldfish, more for common goldfish.
Once you've got the tank and all the equipment then it takes around 6 weeks to be ready for fish. I can go through it all step-by-step if you want, just let me know how big your tank is and I can help you choose suitable fish.
A word of warning about aquatic stores- many of them are not trained and will just sell you any old equipment and fish. A lot of stores sell fish that can reach 2 feet long and/or become aggressive so make sure you do loads of research and never just go along with what the shop tells you! Internet fish geeks are a more reliable source of info 
Hope that helps a bit.