Vegetable-garden-guide.com has the skinny on using containers:

If you have only a small area to grow this vegetable, carrots are great for growing in containers. In the round pots you can harvest between 30-40 carrots and in the larger square and rectangular plant containers you can produce many more.

The advantages of growing carrots in containers are:

1. No poor soil problems if using shop bought compost.

2. No weeding and digging concerns.

3. And no soil pest problems.

What you do need to keep in mind though is a little more attention will need to be given to watering and feeding.

Full carrot growing instructions here. Look how happy she is!