>Should I move along and hope that things get clearer for me in the future modules or should I redo the exercise again and again until I can write it without looking into the solution document?

I believe everything worth doing is worth doing well. So therefore it'll be nice to painstakingly redo the process until you get it. 
You know that joy that comes when you finally get to know what you're doing..i think that's worth the patience and time..