Hi,
First, there are some lovely photos of Aldwincle online - put Aldwincle in the search engine and you should find it. (It won't let me import the site!)
Aldwincle is between Thrapston and Oundle - pretty village.
Thrapston has records for a Baptist church but the earliest Joseph Moore on the baptism record is 17th Nov 1799.
I found a baptism on the IGI for a Joseph Moore at Rushden, which isn't far from Thrapston, it might be the one:
Baptism 03 Nov 1751
Parents: Joseph and Sarah (you might have seen this one already).
The other baptism in 1799 may well be their son - considering Joseph didn't marry Sarah Dudley until 1793.
Hope this helps - good luck!
kind regards,
Paulene.
P.S. This site might be of interest, too:
Look for Sheffield Indexers - they have a link re. records in Oundle - near Aldwincle.