What happens when you go away?
I will not be able to do my lessons for six weeks. Do I lose all my gems/ingots? Do I have to restart from zero?
Nope! Duolingo saves your progress. All that will happen is your streak (those numbers beside your name) will drop to zero. :( And your skill might decay a bit, but that can be fixed with a few practice reviews. Your lessons completed and lingots/gems will stay the same.
Just out of curiosity - is there a particular reason for competely not being able to at least practice (not learning new things)? As it was already said, the main two effects will be end of streak (a bit pity but nothing to really worry about) and a slight decrease in your XP (might result in a drop of your level). What is more important if you don't practice the new skills fade quicker. All the same 6 weeks is not that long so you should catch up quickly. On the other hand you can take duolingo almost everywhere - on your mobile, use another computer (e.g. at the internet caffee). Thing it over, maybe you will be able to keep practicing. One more thing worth considering is decreasing the expected XP to gain daily (to 10). This way you'll be able to keep your streak with just one practice a day.