The integrated graphics on newer processors are better than the high-end GPUs a decade ago. They're certainly powerful enough to for Minecraft. The benchmarks I'm seeing say that the integrated graphics in this processor can hit 50-60 fps in Minecraft at 1080p.
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The biggest drawback of all-in-ones is that they combine the monitor with the computer. A computer is typically obsolete after 5-7 years. A monitor will usually last 15-20 years. So you're needlessly investing your money in something (a monitor) that you'll be forced to throw away while it still has 2/3 to 3/4 of its usable life left.
Personally I'd go for a laptop. The anywhere capability of portable computing cannot be reproduced by a desktop, and the larger screen of a laptop provides something a phone or tablet cannot. If you wish to use it as a desktop, you can always buy an external monitor, mouse, and keyboard. The only drawbacks are expense (both purchase and repair) and (lack of) upgradeability. But streamed gaming is getting to the point where you can run a game on a powerful desktop PC, and stream it to a laptop or tablet for hours of gaming on battery away from the noise and heat. You only really need to play on the desktop if you're a hardcore gamer who wants 144 fps with G-sync.
If you think your daughter will stay interested in 3D gaming, a desktop would let you upgrade the GPU in the future. It's just that at the age most kids are interested in Minecraft, it's impossible to say what their future interests will be. So the upgradeability of a desktop *might* be useful, whereas the portability of a laptop *will* be useful (unless your kid already has a tablet).
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