Right now, ship to ship combat is handled via the basic moves. I believe there is a chapter about it in the game right now, but I could definitely expand on that. Essentially, if you're in a ship, it will have health (usually 7), armor, weapons, etc. If you are in a Y-Wing and want to bomb a Star destroyer, you might need to roll "use the Force" as an "act under pressure" type piloting roll to avoid the Destroyer's canons. Then, once you are in close enough, you might try a bombardment. Your senate would then have you roll Blast'em to see how you do. In my opinion, this works just fine for Ship to Ship combat. Check out the Scout for some playbook moves that help flesh out space combat.
I do have thoughts as to possibly designing Spaceship playbooks, if only so it's easier to keep track of what your ship is capable of. For now, if there's something that happens in a Space encounter that you feel isn't covered in the Basic Moves, feel free to contact me so I can take it into account. The Senate might also come up with a custom move to cover something cool your ship can do. For example The Ghost from Rebels might have a custom move about how the Phantom (it's detachable shuttle) functions.
Thank you for your interest and your suggestions :)