conventional wisdom is to wait to breed them until they are 18 - 24 months old.
I have bred well grown does at 7 - 8 months old. they MUST be well grown and MUST continue to grow (ie have good nutrition) throughout the pregnancy. they MUST be at least 30kg for standards (you can do the conversion to lbs)
I have found that you might not have any choice. We bought a Nigerian that had been with a buck since she was at least 6 months old and it was near to her second birthday when she had her first kid. I have 3 Nubian yearlings in with a buck Since November and I am still waiting. The buck is a juvenile also so that has some to do with it, but the Nigerian was with a seasoned buck and it still didn't matter. She was with him so long I thought she was sterile. The rule of thumb is no earlier that 7 months. That would then put the doe at One year old when she has her baby. When you let her go at it that young you really have to feed her heavy. She has to develop herself along with the kid and then be able to produce milk.
Like the others said it depends and you may have no choice. Comparatively, one of the things you learn in developmental psych is how stressful the pregnancy and birthing process is on human beings (and really I find this to apply to all mammals). A still developing person - i.e. teenager still has many nutritional requirements and can have stunted growth or other developmental issues due to the body diverting some of the energy to the growing fetus that would have been used for the growth and development of the teenager.
Most goats from what I have read stop growing around 3 years, but as long as you maintain the nutritional requirements for both mom and babies you should be fine to start out at around 2 years, give or take. Just remember to make sure of the nutritional needs. You could also do as Chris suggested and start earlier, but again feed heavily, and use caution. Ultimately you decide when to breed your does, but also try to think of their welfare.
CC, pygmies are renowned for birthing troubles (goes hand in hand with their small nature and stocky build).
I have a friend who breeds show pygmies (outstanding animals) and I'd like to contact her and ask her advice, before I say a specific age and/or weight for pygmy breeding.
My go-to gal for pygmies lol breeds her does for the first time at 1.5 yrs old, but said that if they are particularly small she might delay a bit, and always always make sure you join them to a buck that throws small birthweight kids.