Is the rim polished or heat finished?
Is there a "worn" ring around the inside of the neck, which would have made the seal with a stopper?
(evidence that it might be a perfume)
I do not think it is IoWSG either, sorry.
It looks more like a small posy vase than a perfume to me, and has a Caithnessy look about it, but I don't know if it could be Caithness.