Hi mclean124, is this the record of Peter leaving Denmark, that you mean? This is taken from the registry of Danish citizens leaving from Copenhagen.
DDD Danish Emigration Archives
Name: Petersen, Peter
Contract no.: 18900
Registration date: 27-02-1872
Birth place: ?
Last res. parish: Odense
Last res. county: Odense
Last residence: Odense
Destination country: Australien
Destination city: ?
Destination state: Queensland
Name of ship: Indirekte
Odense (the city) in Odense (amt) was the home of Hans Christian Andersen. Odense is on the island of Fyn (Funen). Middlefart is also in Odense amt.
A map here, showing that Odense amt and Svendborg amt share the island of Fyn:http://www.danishfamilysearch.com/
A map here, showing the herreds within Odense amt. Within each herred are parishes (sogns):http://www.danishfamilysearch.com/amt14
Another useful website:www.ddd.dda.dk
Here is the gateway for hand searching the 1870 census in Odense amt. It is not yet transcribed. Middlefart is in Vends herred in Odense amt.http://www.danishfamilysearch.com/census1870/amt14
Here is a copy of a church book for 1863, showing people who registered to leave, but I have not found a leaving list online for 1872 (sometimes some church records get destroyed or lost):https://www.sa.dk/ao-soegesider/billedviser?bsid=17824#17824...
Consider searching for Peter in a confirmation record - confirmation age should be about age 14 or older.