Courts throughout Louisiana have different procedural and evidentiary requirements in how they deal with uncontested divorce cases. Unfortunately, there is no one publication that one can turn to in order to understand the various idiosyncrasies of the individual courts of Louisiana, but rather must be learned through experience and practice.
The general procedure for getting an uncontested divorce is to file a petition in a district court, and then have your spouse sign a notarized waiver of service and citation, request that the court grant you a preliminary default, and two days after (exclusive of legal holidays and weekends) file for a confirmation of default.
Divorces in other parishes, namely Jefferson and Orleans, generally allow for the legal paperwork to be done in around one week. This is because the waiver of service and citation can typically be signed just after the petition is filed and is assigned a docket number. As soon as the waiver is signed, and a preliminary default is entered, all that is required is waiting the two days, exclusive of holidays.
Overall, this is probably a good policy decision because it is strange for a judgment of preliminary default to be entered so quickly after waiving service. For a respondent to waive service, this person is generally doing a favor to the petitioner. However, the vast majority of waivers of service also including additional language making it so that respondents who waive service are losing a tremendous number of their legal rights.
In the end, all this is doing is adding an additional fifteen days to the time that it would normally take for you to end your marriage officially. While it is understandable that you probably want to get the legal paperwork over as soon as possible, waiting just over two weeks should not be that bad.