Would she have to get it dissolved before she started dating again?
Look Ben, not to be rude, but any person you are asking questions for in random fashion on the internet would be better served by sitting down and talking to a priest. Firstly, because specifics of the relationship matter. And secondly, because you are going to get a lot of answers here that are just plain wrong. It’s the nature of EVERY marriage-related question posed here on CAF. Someone comes along and gives erroneous information, not out of malice but just out of their own current understanding.
Regarding such a person “having to” get the marriage dissolved or declared null (both are avenues) before dating, who is the authority here? You asked your question about two non-Catholics. So, there is no one telling them that they “have to” do this or that. And no one to dissolve the marriage or declare nullity.
If the Catholic Church is involved, when it comes to sacramental marriages it is imprudent to get into relationships before freedom to marry is determined, because if the marriage is found to be valid the person is bound until the death of their spouse. Having someone they’ve formed an attachment to who is not their spouse can cause serious heartache and temptation.
When it comes to natural marriages, the Pauline and Petrine Privilege are both invoked as a favor of the faith in a marriage situation, so logically there would have to be a relationship formed before such privilege could be invoked. But note, Petrine Privilege is not a foregone conclusion. One must petition for it.