Here Joseph Smith deleted the pronoun it in his editing for the 1837 edition. One could view his editing as the result of treating “they felt” as parenthetical, as if the direct object complement for “they were doing” was “that which was the duty which they owed to their God”. Under this interpretation, the it unnecessarily restates the subject relative pronoun which.
The original text had a few other examples of redundant it that have been removed from the standard text:
The first two deletions of it were made by Joseph Smith in his editing for the 1837 edition; the third one was made in the 1920 LDS edition. Although nonstandard in written English, the original repetition of the it in these examples (as well as in Alma 43:46) facilitates our processing of the text. The critical text will restore each redundant it, including the one here in Alma 43:46. The other examples are individually discussed in their own place.
Summary: Restore the redundant it in Alma 43:46 (“they were doing that which they felt it was the duty which they owed to their God”).