Less than $1,000 in joint assets? Seriously...just give her EVERYTHING, sign the deal, and walk away. The alternative is to spend thousands fighting over nothing like I'm having to do. If you have to go the contested route (which it's sounding like)...you're both looking at shelling out $5k+ for attorneys to gain jack $h1t.
"Don't worry....I know she's not entitled to anything?" Sorry to say that you're wrong there. If she wants to be a NJ, she'll ask for (and get) 50% of your retirement account (i.e. 401k) gains that were realized during the course of your marriage.
As a point of reference for you...I too was married less than a year. I spoke with FIVE lawyers. All said "this will be a piece of cake," "no big deal," "she's not entitled to anything," etc.

I'm sorry to say that none of their comments...though probably accurate in many cases...account for the NJ factor.
My situation. No kids. I have a house (pre-marital). There's a car in both of our names. I had to leave because in VA...there was literally no way that I was going to get her out of the house early on (had to get a pendente lite judgment to get awarded the house...she's still in it though).
I'm going on five months separated. I paid for EVERYTHING for three months...and 90%+ for the past 1.5. I was awarded spousal support, but have yet to receive a cent. That's the Reader's Digest/short version.
I've already shelled out $4,500 in attorney fees. Who knows what the final damage will be.
Seriously...figure out what she wants and give it to her to make her go away. You might say "this is silly...neither of us have a pot to piss in," but you really have no idea what you're looking at here if she is really wanting to be a NJ and found an attorney that wants to rack up billable hours.