One problem with woodchips, especially those delivered from tree trimmers, is that they can develop some pretty bad mold spores (Aspergillus), especially if fresh and layered thick. I'd let my kids play in a big pile of dry, decomposing woodchips before I knew better, and they started getting lung problems! Here's a study:
https://www.cdc.gov/mmwr/preview/mmwrhtml/00000772.htm
http://articles.chicagotribune.com/1998-08-13/news/9808130065_1_mulch-composting-decomposing
David Denning, of the University of Manchester, said that while Aspergillus itself could be found in many gardens, it would generally be dangerous only if disturbed in large quantities and the resulting dust inhaled.
He said: "This should not be a problem for your average small-scale gardener who is using small quantities of compost at one time.
"However, if you are moving it in very large amounts, then perhaps wearing a face-mask would be advisable."
I'd use sand (if you don't have cats) or, like Anne said, a low-growing ground cover like grass, moss, thyme. Grass is non-toxic, and I'm not so sure about eating moss, so perhaps that wouldn't be a good option for a little one who sticks things in her mouth. There's quite a few edible groundcovers though, and you could grow one or many of them. The ones that first come to mind: chives (can be mowed like grass), pansies, clover, chamomile (don't want to eat large quantities, though), mint (might take over, which may or may not be a good thing), lemon balm, thyme, oregano, dandelions (very edible and fun!), parsley, and self-heal.