The label states give by mouth 0.5ml (1mg) which one do I give?

Is it a liquid?

There is 1 mg in 0.5 ml. You give 0.5 ml.

They should be the same amount, one is weight, the other volume

Chuck is exactly right.

This is a liquid, hence the ml (milliliter)

There is one milligram per half a milliliter. Thus 1mg = 0.5ml. Or 2mg = 1ml, and so forth.