Hi David,
Making portraits outside in the middle of the day is never an easy task.
There are several reasons for this, but the most notable is that the sun will inevitably cast hard shadows onto the subject. You can see this happening on the ribbing of the hat.
Another big problem with photographing portraits in the middle of the day is the mix of bright sunlight and dark shadows, which produces very high contrast. As we can see at the moment, there is a lot of light on the hat, but in the shadow area of the hat there is not much light and the girl's face is rather dark.
Now, the usual approach that most amateur photographers tend to take when it comes to lightening a face in these situations is to add some flash, usually from on-camera flash. Personally, I hate this approach. Unless the flash is diffused with a big soft box, the light becomes very unflattering.
Another option some photographers use is to use a large white reflector, often around 1 x 2m in size, to reflect light into the shadow areas around the face. The problem with this approach is that you need someone to hold the reflector for you. The challenge of getting a three-year-old to stand still, while holding a reflector in the right place and taking the shot may be insurmountable.
Another option would be to select the face in Photoshop (use the Lasso tool with Feather set to around 50 pixels) and then use the Curves adjustment to lighten the skin tones. Slide the highlight marker across towards the middle of the picture, and if necessary move the middle of the curve outwards until the face looks a little brighter.
This adjustment should only take about one minute.
Hope this is a help!
Cheers, Anthony.
Image Doctor's edited version