In my experience the additional information was usually given about 1849, although some parishes were earlier in using the new format. Braddan might have been one of them, because I did use some Douglas/Braddan registers for a while which were much earlier in giving the extra information.
The LDS film number for Braddan marriages 1844 - 1849 is 0106711.

Before buying a copy you could try asking the Registry whether the father's name was given for your date:
www.gov.im/registries/general/civilregistry/

The film would always be worth seeing for additional information if you don't buy a copy.

Sue