A dispensation from form to be married at a JP can be granted when a Catholic marries a non-Catholic for serious reasons pertaining to the non-Catholic.
There is no dispensation possible when two Catholics are marrying.
If you are in the US/Canada, you marry in the Catholic form or get a dispensation from form. You do not marry civilly without dispensation. To do so would be to marry invalidly. One would have to then have the marriage convalidated.
If one is in a country where the priest/deacon is not recognized as civil official as well as the religious official, then yes the couple must marry civilly first-- but is not to live together-- and then very shortly after (typically one or two days) they are married in the Church.
The bottom line is that any Catholic preparing for marriage must make their first stop their pastor. The pastor will outline everything necessary for a valid marriage.