I don't think so, unless you are interested in completely doing comp sci as your next step in life (ie not going to grad school in astronomy). No one will care about if you have a major versus a minor if you already are going to have a physics degree, and frankly a comp sci minor is already ahead of what a lot of folks are going to have.
As for projects you can work on, the best is getting in touch with a researcher on campus you can do research with and try to find a project related to computer coding that you can do. (I realize that's not an option in all countries.) If that isn't an option, maybe do something like this data driven astronomy class on coursera- I hear it's pretty good!