Since I have an associate degree and credit towards a bachelor's, should I negotiate for a higher pay grade on a VA job offer?

Negotiate to a GS-6? No.
Negotiate to a higher starting step on the pay scale? You absolute CAN negotiate for a higher step, but SHOULD you. It's possible if you're not just a 'round peg for the round hole' type of job.

First, if you're not that familiar with the General Schedule classifications and pay, you should read up on it*.

The GS pay scale is much like the military in that there is a base (your rank) and a 'step' (how many years you've been in). Unlike the military though you can sometimes negotiate starting at a higher step (most of the time, but not always, they will offer you a GS-x, Step 1 starting salary).

The bottom line is "what do you have to negotiate with" .. From USAJOBS, here is the comments regarding starting salary, “A new General Schedule (GS) employee is entitled to have pay set at step 1 of the employee’s grade. An agency may also opt to use the superior qualifications and special needs pay-setting authority to hire you with at a higher pay step. Under this authority, an agency may set pay up to step 10. An agency may use this authority based on the candidate’s superior qualifications or a special need of the agency for the candidate’s services. An agency must approve each determination to use the superior qualifications and special needs pay-setting authority prior to the candidate entering on duty. Contact the employing agency for information about its policy.”

You should absolutely check it out .. filling an open job request for the federal government is a long process for you and the agency, so they have incentive to having you accept, so just asking for a step increase isn't likely to tank the offer, but make sure you have your 'sales pitch' ready about WHY you should get a higher starting step.

There's a great LinkedIn article about getting your ducks in order regarding asking for a starting step increase you should read (https://www.linkedin.com/pulse/what-superior-qualification-special-needs-pay-setting-angel-castro).
-----------------------------------------------
* https://www.opm.gov/policy-data-oversight/pay-leave/pay-systems/general-schedule/

Unless you have some experience that directly relates I don't think you are likely to get a better offer on this position.

GS positions much like Military positions they are based on rank. What is the rank for the billet you were assigned? If you were hired for a GS-6 position that is the pay grade for that position. But if the position is a GS-6/7 position you have the potential for promotion beyond the standard step promotion.

I am a GS-11 and if I want to be promoted to 12 I will need to apply and be hired for a GS-12 position.

With all that said what is the AA in? Unless it is directly applicable to the job field I wouldn't expect a promotion just for having the degree.