Oh, wow they really are very tiny aren't they! Do they get a lot bigger than that? If not I wouldn't think they could cause enough damage to worry about, either.
If you want a good, organic control for leaf-feeding caterpillars, Bt is your answer. It's available as a concentrate at any garden center, and can be sprayed on right up to day of harvest. Non-toxic except to a caterpillar that actually eats a treated leaf.
edited to add: I asked on the Butterfly forum which ones use carrot as a host plant. Will get back to you on this.
