A Nikon is all good but if you're willing to look into other brands I would definitely suggest a Canon T2i
I honestly don't know all that much about Nikons but if you were to consider going with the T2i, I can say that I have one and know first-hand that it's very easy to use but also very pro. I doubt she would have much of a problem "getting it to take good pictures" seeing as with this camera it's not all about dozens of buttons and effects; it's more about taking a second to match the current light with your ISO and getting a good angle for whatever you're taking a picture of.
It also has movie mode, which comes in handy.
Seeing as you're looking into a professional career with this camera, and I doubt she would want a point-and-click, keep in mind that this camera seems very easy to use but is very professional. Movies are shot with this camera, commercials are shot with this camera. Professional photographers use this camera all the time and the results are phenomenal. If she's going to do wedding photos and the like then this camera is still one of the better choices.
I bought mine with a standard zoom lens and it does a pretty good job. Depending on the light it can get a little grainy when zoomed to its deepest point but on a clear day the image quality is impeccable.
However, it does have its downfalls. It doesn't do well with darker skin (but a LOT of cameras don't) or nighttime, whatever the lighting. I just did a test with my standard zoom lens and taking a picture with the shutter speed at 30, the ISO at 3200 (I usually keep it below 800 but it's evening and the current light calls for a higher ISO) and aperture at 5.6, the photo is bright with limited grain, or so it seems. Zooming into the photo the surface image quality quickly decreases. I would say this camera is more of an outdoors camera, which is mostly what I use it for.
I do agree with Azuremen about wedding photos, etc. being more about the lens selection. This camera is in the
$600/$700 price range so you would have a lot of money left over for a really good lens.
The others posting here seem to be giving you some pretty good suggestions for a Nikon so I guess I won't have to go into that considering I know almost nothing about them
Also, a question about the current camera. Could
definitely be defective by the sound of it. But not getting good results with the 60D might not be because there's something wrong with it. What shutter speed does she use? Certain shutter speed/ISO combinations will always result in a hot mess, tripod or not.
For example, to brighten my image I just took a photo at 800 ISO, shutter speed 0"5. Slightly blurry.
ISO at 3200, shutter speed at 1"6. Result = a bright blurry mess.
ISO at 1600 and shutter speed at 15 gave the photo the kind of light we all find attractive
and kept everything in non-blurry focus. Sometime's more or so all about what the photographer does with certain settings, not the camera/lens itself.
Hope I helped with this giant pitch, lol. Good luck with her photo career, sounds like she's on the right track