Just the feeling that I get from what people from other systems say, first is generally not an instructor rank.This would depend on specific clubs and systems.
As to whether or not some schools put first dans into an instructor roles or whether or not first dans should be instructing is different subject.
I thought you were Kukkiwon.For TKD, 4th dan is considered an instructor rank, but in our system, 1st dan is an instructor rank as well.
Daniel