It seems like your counsellor isn't overly alarmed about the symptoms (seems satisfied you've described your depersonalization symptoms well and doesn't believe it is psychosis) and has given you some strategies to help with it. When it happens do the grounding techniques help it? What is your gut feeling? Do you think something more is going on?
I agree with Skeezys that the GP will probably not know and the psychiatrist will be mostly concerned with diagnostic labelling and drug treatment. Is that something you would like to happen?
I agree with the suggestion of perhaps seeing a psychologist or someone more knowledgeable than a garden variety counsellor to help with the dissociative issues.