Actually my first camera/lens combo was the 17-55mm 2.8 with an XTI. And I also bought an external flash at the same time.
I suppose it depends if you're buying a DSLR to use like a glorified compact camera or if you're buying a DSLR because you're interested in learning the art of photography.
I bought a good camera/lens because I was interested in photography and wanted to take really nice pictures of my kids, just like the OP. I suppose it's all about how much effort you want to put in. It's the old story though that a better camera won't make you a better photographer. The problem with kit lenses is that they just don't do anything that a compact can't do almost as well, so when you ask on a forum photographers recommend more expensive lenses because they allow you to experiment with photography more.
You can't take photo's like these with kit lenses and no flash.
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Even kit lenses and an entry DSLR are quite forgiving, in terms of ISO and shaky hands.
You might need a faster lens to get those photos, but the camera shouldn't matter. The exports you posted look very good (due to the good light, fast lens, and good photography), but they have less megapixels than a cheap camera-phone picture. I think better camera will only be noticeable if you blow the photos up, or print them, or take photos in very poor light.
A cheap (~$100) 50mm prime is great value, and very good at what it does (animals in the zoo? head and shoulders photos?), but not too practical for family photos. You could also look for a cheap (or second-hand) prime in the 20-30 mm range. Expect to pay >$300.
A Canon EF-S 17-55mm f/2.8 IS USM Lens would be a massive upgrade, but it costs > $1000. The Canon EF-S 15-85mm f/3.5-5.6 IS USM is a good value "general purpose" lens, but it's not cheap either.
A >$50 macro adaptor is fun, if you want to play with a wide lens but aren't sure you want to drop $1000 on a real lens yet. But never ever admit doing this around serious photographers.