This may just be a personal preference, but I'm not a huge fan of all-in-ones. I much prefer a conventional tower. There are a number of reasons for this: all-in-ones are generally overpriced, it can be difficult to upgrade components in the future and if the monitor malfunctions you have to pay for a screen replacement.
I'm not going to say it's a terrible PC for the price. It's decent, although you can likely find better systems for less. This system is geared more towards the average user than any form of gaming experience.
The biggest thing that would turn me off is that this system (and typically all-in-ones in general) lack a graphics card. A graphics card is something that's highly recommended for any gaming. It's also important to think about the future. Sure, your daughter likes Minecraft now, but there's no telling what games she will want to play in the future. As time progresses, a graphics card is becoming increasingly important.