Ask Mr. Smarty Plants

A look through the internet for cottage yarrow turned up some references to this name being associated with the native plant, Achillea millefolium (common yarrow). It appears that florists often refer to Achillea millefolium cultivars as cottage yarrow.
Yarrow can be propagate from seed. Leave the flat-topped seedheads on the plant after they flower. The seed is light tan when it is mature.  The seeds will be mature in late summer or early fall. Collect the entire inflorescence (seedhead) and carefully tip it into a paper bag. Tie the bag around the seedhead and hang the plant upside down in a warm, dry location to fully dry.  Once dry, rub the seedhead lightly to release the seed from the chaff. Store the seed in a sealed glass jar in the refrigerator until ready for sowing.  The Native Plant Network indicates that common yarrow seed will be viable for 3-5 years when stored properly.
You can sow yarrow seed in the fall outdoors if a garden bed is ready. Or the seed can be stored in the refrigerator and sown in the spring (indoors in seed flats or outdoors in garden beds).  Common yarrow is also very easy to propagate by dividing the plants. The plant produces underground shoots called rhizomes that often root and can be severed from the plant, potted up and grown on for later transplanting.
Queen Anne’s lace (Daucus carota) is native to Europe, but has naturalized to North America and Australia.  Wikipedia has the following information about the seed production for Queen Anne’s lace.  "After fertilization and as seeds develop, the outer umbellets of an umbel bend inward causing the umbel shape to change from slightly convex or fairly flat to concave, and when cupped it resembles a bird's nest.
The fruit that develops is a schizocarp consisting of two mericarps; each mericarp is an achene or true seed. The paired mericarps are easily separated when they are dry. Premature separation (shattering) before harvest is undesirable because it can result in seed loss. Mature seeds are flattened on the commissural side that faced the septum of the ovary. The flattened side has five longitudinal ribs. The bristly hairs that protrude from some ribs are usually removed by abrasion during milling and cleaning. Seeds also contain oil ducts and canals. Seeds vary somewhat in size, ranging from less than 500 to more than 1000 seeds per gram."
Interestingly, there is a North American wild carrot, Daucus pusillus that is often mistaken for Queen Anne’s lace. Wild carrot blooms in flat clusters; when flowers pass, pedicels turn upward into a birds nest; when seeds ripe, spreads open again facilitating adhesion to passing animals.
Queen Anne's lace has a deep purple central flower.