All Apiaceae are biennial, which means they must be over-wintered before producing seeds during their second season. Mostly they are best planted in Spring or Summer for seed the following Summer.
Apiaceae cross within species but not between different genera. i.e. carrots will cross with other varieties of the Daucus carota species, which includes the wild carrot, but will not cross with parsnips, for example. Isolation of 1/2 mile is required for pure seed from varieties of the same species and 6 plants are required to guarantee you are maintaining genetically strong seed.
The Apiaceae family are all insect pollinated. The flowers are perfect (they have both male and female parts), but they cannot self pollinate because the anthers shed their pollen before the stigmas are ready on each flower. The flowers open on each head over a long period of time however so there are always stigmas ready to receive the pollen that is being shed by another flower.
Because the flowers are insect pollinated, each crop must be isolated from other members of the same species, theoretically by several kilometres! I find that it is possible to grow carrot seed outside and not have it crossed by wild carrot with a little careful planning, especially in hilly areas, where the winds and the bees tend to operate within valley systems. We have successfully saved good seed by planting a patch of carrot seed inside a large area of tall corn. The carrot usually goes to seed before the wild carrot and then by the time the wild carrot flowers the corn is high.
I would recommend playing around with ways to make it work, making sure you have minimum numbers of around 60 plants but even better for the long haul several hundred. Last year we collected seed only from the heads that set early on the carrots because we noticed that they set before any wild carrot was flowering.
Carrot seed is usually grown using the seed to root to seed method. Seed is planted in Spring, the roots are harvested in autumn, when you can check them all and keep the most true to type to plant again for seed. In a mild winter they can be replanted immediately – in a cold climate they are usually stored in sawdust for the winter. The roots will go up to seed fast in Spring. The first seed heads are always the largest and the strongest. They can be harvested as soon as the heads turn brown and are then best dried until very dry in a greenhouse or drier. We rub our seed heads across seed screens to clean the seed but it can be done by rubbing or dancing on the seed. The more you rub it the smoother the seeds become.