I'm a 2nd year university student, and I thought it would be a good idea to expand my abilities. I will be using python later this year to complete a gui for a  C program (using Tkinter), but I want to make a side project as well, and python seems like a great language to do it with. 
I want a project which has multiple levels for me to code, so it's definitely going to have a gui and command-line version, and then maybe some database stuff (since I would like to know more about SQL and other database tech). 
I thought I could make a music player. Start by just making a command line program which plays a music file, then expand it from there, probably using pygtk for the gui.
Considering I have no python experience, but I do have a strong background in C and Java, are there going to be any difficulties which will unexpectedly stop me? I have never made a music application before, and I am not sure whats involved in keeping a music library, for example.
Are there any other projects you might recommend, that can be completed in about an hour a night, for 3 months? (Or get a significant working program out of it, even if its not complete).
Thanks!
Considering I have no python experience, but I do have a strong background in C and Java, are there going to be any difficulties which will unexpectedly stop me? 

Yes. 

I have never made a music application before, and I am not sure whats involved in keeping a music library, for example.

That will stop you.
Want advice?  
Step 1.  Avoid asking yes/no questions.  
Step 2.  Start smaller.  [see below]
Step 3.  Start with a tutorial on Python.
Step 4.  Find related projects, download their code, and read it.

On Starting Smaller.
"about an hour a night, for 3 months".  90 hours.  
Allocate 40 hours to do enough Python tutorials to understand the language.  Ordinarily, I'd suggest 80 hours for this, but your budget is tight.
Allocate another 40 hours to working out how the sound playback API's work on your platform.  This may be too much time, but there are always odd mysteries.  OS API and Device Driver issues are often difficult problems to solve.
Allocate another 40 hours to make enough mistakes to get a PyGTK application that runs respectably well.  Ordinarily, I'd allocate at least 120 hours to this, since GUI design includes lots of new concepts, not covered in the language tutorials.   Again, your budget is tight.
Learning SQL and Database design and an ORM API.  Perhaps 40 hours.  There are a lot of mistakes you can make here, and you'll need time to make those mistakes.  
Allocate another 40 hours to creating some kind of "music library" built on existing file system API's.  This involves defining some use cases for add, change and delete and figuring out how to implement those use cases.
That's my rationale for suggesting that you may want to "start smaller".
A good side-project for learning python?