I want to register as a non-profit org., but I'm not sure how it'd work because I'm leaving in a couple months to work in Asia for a year or more.
My website is for international photography if that helps. I can't seem to find an option for an online-only non-profit, which would be perfect. Is there an option for something like this?
Plus, I'd like to be eligible for donations, of course.
Any advice would be great.
A non-profit is just a regular company, it just has to comply with additional set of rules to be eligible for non-profit, tax-exempt status. Those rules vary by state. See http://www.councilofnonprofits.org/howtostartanonprofit for the minimum basics on establishing a non-profit.
In that respect it doesn't matter where you are located, physically, as you would be just an owner and/or employee of that company.
That being said, judging from your question, you seem to have serious misunderstanding of even the basics. For example, you don't register as a non profit - you create a company and then apply for a non-profit status as a company. Similarly, there is no such thing as online-only non-profit just as there is no such thing like online-only corporation.
Obtaining a non-profit status is hard. Government makes money by taxing corporations. Non-profit status means corporation don't have to pay taxes. Government doesn't like that and sets a high bar for giving non-profit status. Government requires a lot of paperwork to obtain non-profit status initially as well as to prove, every year, that you're still eligible for that status. This is the kind of paperwork that you're very unlikely to complete without the help of an accountant and a lawyer that specialize in that area. It's also costly.