At every stage of the process you should be learning songs that match (or slightly challenge) your current skills.

After all, that's the purpose of lessons & practicing, to play music!

The mini-songs are a great & practical way to do this.  The instructor can focus very specifically on certain ideas & skills in an organized curriculum.  But eventually you have to apply all those ideas & skills to the music that you want to play.

So, find a couple of songs at your skill level & start learning & playing them.  And them into your practice routine.  Being able to play through an entire song in tune & in time is an absolutely necessary skill. 

Hope that helps!