I imagine there has to be more than just that random rock ledge on their planet, right?
Probably not. After all, the Founders would want to keep the Dominion as far away from them as they possibly can!
They certainly wouldn't want to build any Jem'Hadar or Vorta there, let alone ships or weapons - all they would really need is a communications room for contacting a select bunch of Vorta in the Dominion proper, and telling them how to run the show. We see some facilities on the first hideout world, namely those used for interrogating the Defiant
captives, and some Vorta there, but there might be very little else on that planet besides the big seas of Founder goo and the few inspirational rock outcroppings sticking out of the seas.
I guess what I'm thinking is... how did they first get off their planet? We've seen Changelings become birds and fly around but can they fly through space? Or would they require some infrastructure on their homeworld to develop technology and build ships? I can definitely imagine them not wanting to 'build' Jem'Hadar and Vorta on their Homeworld now (heck, they probably don't even allow them to visit). But how does a species with (seemingly) no infrastructure on their homeworld at all develop the technology to rule an entire quadrant? Do they even have weapons? What made the big pool of goo so scary to everyone?