Good on you two.
Be very very careful - you have taken your first step towards financial ruin and artistic frustration

.
But seroiusly I wouldnt worry too much about improving your first image (which by the way is far far better than my first ever image) get out and take as many images piggyback as you can to start with. Yep Daid is right repostioning the camera would help - playing with focus will help - find where focus is best (shoot a series and have a look) - play with framing etc etc etc.
You can get tips off people with more experience (I am sure most people here are happy to help) but by experimentation you will develop into your own imager that is a composite of advice and your experience.
Congratulations - you have done somethinig very few people have ever done relatively speaking - ie taken an astrophoto that is worth keeping - (keep your first and keep referring back to it and you will se how you develop)
Good luck and keep going
Mark Bolton