For a niche field that programmers rarely ever hear much about, there's quite a breadth of variety.
Lots of people are hired into aerospace straight out of college, with degrees in non-aerospace things like computer science and electrical engineering. A lot of the domain knowledge is hard to come by outside of working in the field, and it's generally not expected for an entry-level role.
But even if not strictly required, some related domain knowledge would sure make you shine as a job candidate. Specifically:
- Lots of software is written in C, C++, or (less often today) Ada. I would suggest focusing on being skillful with C first and C++ second. It would be nice bonus points to at least have some familiarity with Ada, even if the most you ever do with it on the job is read old code. Verification test frameworks will likely be in some high level scripting language; I've seen Python and Lua used, myself. Model-based development tools (like Simulink) are used sometimes too.
- Understanding of real time embedded systems would be great. There are a variety of such systems out there; real-time Linux would be a good option to become familiar with.
- Knowledge of low-level networking concepts. I.e., the bytes that make up UDP packets, TCP packets, packet headers. Whether if you work directly with networking or not, you'll likely encounter "one box sending data to another box" all over in aerospace. Good ol' Ethernet is used, but so are other more obscure protocols like ARINC 429, ARINC 664, MIL-STD 1553, etc. While most of these specs are not available free of charge, they are available to the general public. They're not exactly light reading, though, and I've learned more with the spec in one hand and a packet sniffer on a running system in the other, than trying to comprehend the spec by itself. But Ethernet / TCP / UDP is easy to learn about, so start there.
- Aerospace science? If you went out and got a degree in aerospace science, especially a combination of aerospace and CS, I can imagine companies tripping over themselves to hire you. Do you need it to do the job? Depends on the job. You could have a successful career developing software in aerospace without actually knowing much about aerospace, because there's just so much to do. One developer does the aerospace calculations, and another one tackles making the code thread-safe, and so on. But a solid understanding of aerospace science concepts would make you quite desirable as a candidate, and would open doors for you to work on things that other "CS-only" people don't know how to do. [There are some aerospace classes on edx.org -- if you like online courses, could be a good way to start. The University of Kansas has an extensive program, though I don't think they offer it online.]
- Related, and maybe easier (or maybe harder), would be to learn about flying. A ground school class would be a good start, and can be done online. Holding a private pilot certificate would be some great resume fodder, and would also give you good knowledge for the job. You would have better understanding of another facet of aerospace knowledge, and would also have more of an "end user" kind of perspective. [Look at http://www.kingschools.com/ for some online materials, or try a local flight school. Quick start: try X-Plane.]
Any or all of that would be good material for being a more attractive job candidate. But again, many people get their start without knowing much or even any of that, and pick up what they need on the job, so it's not strictly required. It would just be helpful. And, depending on the job market at the time, it could be extremely helpful.
And to restate my opening remark, there is immense breadth in this seemingly tiny niche field. Due to the very nature of the work, no one person does everything. You would almost certainly not do the aerospace calculations, and do the network programming, and do the verification testing, and do the graphical displays, and do the air-to-ground communication system, and do the ... And that's just for the software! Someone designs the nose cone, and the wings, and the fuel system, and the passenger seating, and the ...
As always, beware career advice from random people on the internet. But I hope you found something helpful here!