Well, Achillea millefolium - Yarrow, is listed as a safe plant for turtles to eat, so I think it would be ok for beardies, too.
Yours is not the only dragon who likes to eat strange things, Emmy hates veggies, but goes wild for any kind of weed/green in my yard. Half the weeds I cannot even identify, but they are fast when they want something. The last ting she ate was Mallow, so I know that is safe.