I’m a student from Canada going into grade 11 (junior year) next year. I plan on applying to top American universities. I know that these universities look for rigorous course loads and like to see that you are challenging yourself. The course I would plan to self-study is AP stats (and maybe Music Theory considering I have most of the knowledge already). I managed to take one grade 12 stats class (not AP) a year early and I believe it would help me.
Since minimal AP courses are available in my school, with the majority of them being only available to seniors, would it make sense to self-study AP courses and take a spare period? Or would it make more sense to take normal courses but fill my schedule up.
Thanks! 
Colleges would rather see that you have a rigorous courseload within the framework of your school’s offerings. If there are no AP classes offered to juniors, they are not expecting you to self study some to make up for it.
While skieurope is probably right, APs can also help you get college credit or skip easier classes once you get in to college. Self studying is definitely a possibility; lots of people do it and there are dozens of threads about it on this site. If you decide to go that route, check out http://www.appracticeexams.com and other sites with notes and practice tests. they make the process much easier.
For music theory specifically (I took it last year), it is a lot of listening and transcribing by ear, not easy things to learn even with the help of an experienced teacher. Unless you have prior experience specifically with common-practice era theory (chorale writing, 4-part harmony, chordal structure, etc.), I would not recommend self-studying this exam. AP Stat would probably be a better pick for you, and it is MUCH easier.