I think the answer could only truly found by asking Shakespeare, which leads me to another conclusion, Shakespeare as puppet-master prevents this from being possible.

Shakespeare could have had Juliet run away with Romeo. They were together the morning he left for Mantua. She would have been protected and cared for by Romeo. But if Romeo would have allowed this to happen, the story would have been a happily-ever-after instead of the tragedy he was going for. Also, because of what happens a lesson is learned. The Prince tells both the Montagues and Capulets in the end

See, what a scourge is laid upon your hate,
That heaven finds means to kill your joys with love.

The prince points out that their fight isn't worth it any more. The consequences are too extreme. We need to learn from his advice as well and drop the bitterness that we have in our relationships.

In my opinion, what is preventing her is her parents.  She can't just get up and leave and join Romeo because of them.

You have to remember a couple of things.  First of all, she's only 14.  And this is in a time and place where I doubt she was carrying money around to get her to Mantua.  In addition, women just didn't go around alone in those days.

Second of all, her parents don't know she's married to Romeo.  So it's not like they're going to say "okay, you're his now, go to him."

Maybe she should have told them and maybe they would have let her go then.  But I imagine she didn't want to tell them just then because of how mad they would get.