Welcome!
I love that pony cut. Too cute!!! There's another member here with a Labradoodle, Sophie. You might enjoy that. I think it's a great mix...lab or golden with poodle. I can understand how you are enjoying your dog so much. I have worked with one Labradoodle and he was a joy. And have met several others...but haven't met a Goldendoodle yet.
True, they aren't necessarily a breed. And at first, when putting two different breeds together, they are a mix or if no good, sound, scientific breeding methods are used, they keep on coming out irregularly. But when it comes to the point where repetitive homogeny in the offspring is achieved, the mix can be called a breed rather than a mix or mutt. It is called "fixing a breed." This has happened with some breeders (I think primarily in Australia) with Labradoodles. Labradoodles are a recognized breed in those situations. No, they don't have to be recognized by a club. But it is how all breeds started out. Trial and error, a period of time where there was not much uniformity and then finally fixing the breed.
Anyhow, welcome and can't wait to see lots of pictures.