Hey Hun

Are you referring to the 'Better Access' Initiative? Not sure if its the same thing you are talking about or it's different. But if you google that you should get some helpful info.
Yes, a GP does need to make some sort of diagnosis for the referral (out daughter's is Separation Anxiety) so that may be perhaps tricky for your little one just yet. However definitely get all your courage together and grab DH and go and see another GP. It can be very overwhelming speaking about this sort of stuff with a GP and trying to explain everything to them, but hopefully you can find a good understanding doctor (they do exist but can be rare to find!) somewhere.
All the best.