I think you should still write the letter. That costs nothing but time. You can point out that the incident was reported to the sheriff and that you have eye witnesses who can testify that the dog was not under control/not leashed as is required and ran out at you, causing the fall. You are asking only for the direct costs you've borne to be covered and you hope the owner will do what is right in following through on his/her word.

The last part is key -- making this an issue of honoring one's word and doing what's right. I read years ago that collections letters which use language which invokes "doing what's right" (probably better phrased than that) are more successful than those that simply say "pay up, you deadbeat!" Not as much fun to write as the "pay up, you deadbeat" letters, however!

I'm glad you were not hurt (and glad the dog wasn't, either), and hope you get your costs covered!