I usually wait until they have good size second leaves. Don't get too carried away as you will probably end up with hundreds of the seedlings. They have come up like weeds in my garden and most of them are white. They can throw up some unusual colours when they cross fertilise with parents of a different colour.

When/if you do decide to move them either do it when they are very small or as Jimmy says wait until they are well grown. They absolutely hate getting their roots dry so I take a bucket of water with me and drop them into it when I lift them.
Autumn is advised as the best time to move mature plants.
I take babies about now as they have just begun to grow.

Thanks for all your advice :)