Mary,
Although many of Northumberland's church records (films of original registers)are held at Northumberland County Record Office, several records are also available elsewhere ( e.g. online on sites like GenUKI, familyseatch etc, libraries, etc.)
For example the records of Alnwick Parish from 1777-1890 are available on Familysearch site, within the Durham Bishop's Transcripts section.
If you access this site, on page 136 of the 1516 pages, you can see baptisms for the beginning of 1804... there is no sign of a Dixon baptism.
These are films of the lists of baptisms/marriages/burials from Alnwich Parish, that were periodically copied and forwarded to the Bishop of Durham.
" Parish" means Anglican/Church of England. What religion was your Dixon family ?
Michael Dixon
Newcastle
(Although I am a Northumbrian, my Dixons were fairly recent newcomers from Cumberland)