The best image quality you'll get from the QX10 is when shooting close-ups. The camera can focus as close as 2 inches from a subject at the wide end, and 3.3 feet when zoomed in. This is a crop taken at 75 percent of pictures 18-megapixel resolution at ISO 100. At 100 percent there's just a bit too much noise to make it usable for huge prints or heavy crops.
Despite having a Program mode, you get no control over ISO settings -- only white balance and exposure compensation. For still subjects, you're better off using the camera's Superior Auto mode for handheld shots, unless you're really getting bad results from the auto white balance. Though you might not see much of a difference at this small size, the SA mode uses a multishot process that reduces noise as well as blur from hand movement. (You can view these images at full size later in this slideshow.)
The one big feature smartphone manufacturers haven't really solved yet is optical zoom. (Sorry, Samsung, the Galaxy S4 Zoom doesn't count.) The QX10's gives you a decent range of 25mm (top) to 250mm (bottom).
Having a camera that is remotely controlled by your smartphone allows you to frame up your shot just right for self-portraits. However, there are several cameras from Sony, Panasonic, Nikon, Samsung, and others that can do this, and they don't always need to be connected to your smartphone.