According to Tenn. meat goats, a quick way to treat is to paint 7% iodine on her tail web. then I would offer free choice kelp will allow the goats to eat what they need and so over doseing is not a worry..also sprinkling iodized salt on her feed until the goiter goes away would be safe..
The article also says " Cobalt deficiency and its accompanying Vitamin B12 deficiency can also cause goiters." Adding B complex PLUS which is a good source of 12 could be given daily as well in case the goiter is from that...
she also mentions certain plants that can cause Iodine deficiency , so take a look at her list and see if you have any around
