The use of miniatures and a black backdrop has always been one of my favorite methods of showing space.
Greenscreen/CGI rarely looks natural, and unless done well, just can't beat the simplicity of this method.
Backyard is right, adding some starts would be nice, and that's a great way to do it. Just don't over do it.
Squid did a great job keeping the stars out of focus and subtle, so you may wanna look at that for inspiration.
Honestly, their absence gives a certain sense of emptiness and loneliness which is kinda cool, but it does leave a lot of emptiness in the frame that doesn't look appealing.
Great job on the lighting, that's a one-lamp set up right? The deep shadows look fantastic.
The movement needs to be slower and more smooth to look space-y, could you get one rig to spin the ship, and another to move the camera? When I did a similar shot in my Doctor Who film, I found moving the camera and leaving the ship still looked smoother than vice-versa.