This is actually somewhat of a grey area. In NJ a DUI is not criminal conviction. It is a motor vehicle offense. However, the questions states everything other than MINOR traffic violations. They probably do want you to disclose it, but if you stuck to the plain meaning of the application the DUI is not a criminal offense. There is plausible deny-ability.
Living in NJ shouldn't impact your ability to expunge it. I'd suggest calling an Alaskan DUI attorney to inquire. Beyond that, I generally suggest erring on the side of disclosure. Good luck.
I would consult an experienced DUI or Post-Conviction attorney in Alaska. Typically most states have some kind of relief available in this situation. Good luck.
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Even if it were "expunged" you would still have to disclose it and most agencies and employers will find out about it. So don't try to hide the fact you have a DWI just disclose it and understand that it will be harder for you to get a job than someone who has not made that mistake.