Previously, I have used wood chips but this seems like something a small dog could choke on.
What Is a Dog Friendly Mulch?
Certified GKH Gardening Expert
If you have issues with your dog eating mulch, look into a mulch that is not treated with manure. I have had this issue in the past with my own dog. They are attracted to it. Normal wood chips should not attract them to eating them and they should be fine.
Avoid at all costs cocoa hull mulch. It smells like chocolate (which dogs like) and can be very lethal to them.
You can also try a larger, chunkier wood mulch or a rubber or stone mulch. These don't break down well (or at all) but would be harder for a dog to eat.