Yes, you have a pre-gray tank Airstream. Dumping gray (sink/shower) water on the ground was fine then, but is frowned upon now. But it is dish soap and regular soap, and a few food scraps, perhaps. When was the last time anyone got excited about anyone else washing their car and letting that soap run and enter the ground? But I digress.
As mentioned, you can use a portable tote (blue boy) to cart away your gray water to the dump station, or add a subfloor tank. I added a tank to my '64, and have my tank made for my '61. I utilized my resources and had my tanks tig welded from aluminum...but many aftermarket plastic tanks in various sizes can be custom ordered from suppliers on the internet.
And one other thing about combining the gray/black tanks. Not only would the tank fill up quickly, but if you ever overfilled and had some backflow into the lowest point (usually the tub drain), you would only ever want that to be gray water. Never black water.
"The difference between vintage and retro is that vintage is honestly old and cool. Retro tries to be but isn't."