The Summoning Power Profile had a Summon Vehicle power with the vehicle bought as per equipment but with 15 point per rank of Summon. It wouldn't be a huge conceptual leap to do the same thing with an HQ. You'd want the Controlled Extra, since I assume it's all controlled by you and not independently sentient.
You would also want to Increase Duration to Continuous or it'll all vanish when you take a nap. That's 4 points per rank, and all of the sample HQs are between 5-30ep, so you could easily make any of them with a rank 2 Summon costing 8p total, which is easily small enough to fit into any standard Force Manipulation Array. Actually, you could just power stunt it every time and rest inside.
Of course, you'll want to impose some limits on the design so that it fits the setting and doesn't unbalance the game. The size of the HQ shouldn't be too much larger than what you can make with your Create power, and it definitely shouldn't exceed Toughness. The Features should also make sense based on the descriptor of your Create: simple things like Living Quarters or a Gym would be relatively easy, while advanced electronics or a fully stocked lab might be trickier. Since it's a solid-light construct, maybe you can make really good hardware or even personnel, but you probably couldn't make food.
As a GM, I'd be very careful about things like using the HQ's Defense Systems or other effects for combat. It might be reasonable to put the Slow Flaw on the HQ so it takes a while to create and can't be done in combat.