How can I move a Spatialite table from a Spatialite db to a PostgreSQL db using ogr2ogr?
And, after a bit more reading the ogr2ogr help I found the answer more easily than I expected.
ogr2ogr -f "PostgreSQL" PG:"dbname=db" spatialitedb -sql "SELECT * FROM table" -dialect spatialite -nln new_table
EDIT: As suggested by user30184 in the comments a cleaner, simpler method is:
ogr2ogr -f "PostgreSQL" PG:"dbname=db" spatialitedb spatialite_table_name