Nope. If you want her to come with you, you must get married. Only spouses are recognized by USCIS as legitimate partners of J-visa holders, not girlfriends or fiances.
If you do get married, she can apply for a J-2 visa based on your J-1 visa, which would allow her to accompany you and also look for employment (if she fills out an additional, different, application).
USCIS - Exchange Visitors