If you have the exact date of birth, the next step is to understand the local history.
According to the on-line Historisches Lexikon der Schweiz (http://www.hls-dhs-dss.ch/index.php
), Leibstadt, in the Canton of Aargau, has a complicated history. The complications involve the fact that it was historically two separate villages, Oberleibstadt and Unterleibstadt, separated by a creek. The two halves belonged to different feudal districts. As for the church, it appears to me that these two villages were part of the (Catholic) parish of Leuggern until 1879 or 1880. After 1798, there was probably a Protestant church in the area as well, but I was not able to locate any information in a quick search.
Church and civil registration records after 1875 are generally not open to the public, due to very strict Swiss privacy laws and an entrenched bureaucracy. Church records before 1875, some as far back as the late 16th Century, are frequently available on microfilm through the Family History Library in Salt Lake City, as are any civil registration records for the 19th Century up to 1875. Check the library catalogue on the FamilySearch.org web site. If the library has the microfilm, you can have it sent to your local LDS Family History Center for a very small processing fee -- by far the best, easiest, and least expensive approach to Swiss genealogy.
Unfortunately, it looks like Leuggern is one of the parishes where the Family History Library was not able to microfilm the records. The original records are probably in the cantonal archives of Aargau. Check for a web site, but most of the Swiss cantons have not yet made their church records available over the internet.
Since your ancestor left Switzerland relatively recently, you might be able to obtain information from the government of the commune of Leibstadt: see the web site at www.leibstadt.ch
. A query asking if your ancestral family still lives in the area might get forwarded either to someone of the same surname, or to a local historian.
Good luck with your search!