D&C 20

After baptism, it is given that one who holds the Melchizedek priesthood (elder) under the direction of the bishop who holds keys to this ordinance, is -

"...to confirm those who are baptized into the church, by the laying on of hands for the baptism of fire and the Holy Ghost, according to the scriptures..."  (Doctrine and Covenants | Section 20:41)

What I find interesting was in the Lord's initial instructions was -

"The duty of the members after they are received by baptism.—The elders or priests are to have a sufficient time to expound all things concerning the church of Christ to their understanding, previous to their partaking of the sacrament and being confirmed by the laying on of the hands of the elders, so that all things may be done in order.
69 And the members shall manifest before the church, and also before the elders, by a godly walk and conversation, that they are worthy of it, that there may be works and faith agreeable to the holy scriptures—walking in holiness before the Lord."  (Doctrine and Covenants | Section 20:68 - 69)

It almost sounds like that there must be some waiting time period between baptism and confirmation for teaching, expounding, and the manifesting of worthinesss  But I don't necessarily believe that was to be the intent.  The statement of "The duty of the members after they are received by baptism" suggests to me that this teaching and learning was not only related to immediately after baptims but was considered to be an ongoing process of being a member of the Church and in coming to better understand the Church of Christ as we continute to partake of the sacrament.  We read that to qualify for baptism in the days of Moroni that -

"...they were not baptized save they brought forth fruit meet that they were worthy of it.
2 Neither did they receive any unto baptism save they came forth with a broken heart and a contrite spirit, and witnessed unto the church that they truly repented of all their sins.
3 And none were received unto baptism save they took upon them the name of Christ, having a determination to serve him to the end.
4 And after they had been received unto baptism, and were wrought upon and cleansed by the power of the Holy Ghost, they were numbered among the people of the church of Christ; and their names were taken, that they might be remembered and nourished by the good word of God, to keep them in the right way, to keep them continually watchful unto prayer, relying alone upon the merits of Christ, who was the author and the finisher of their faith."  (Book of Mormon | Moroni 6:1 - 4)

So obviously, much of this expounding and manifesting of worthiness would and should take place before baptism and qualify one to be confirmed and receive the Gift of the Holy Ghost according to these instructions after baptism, with the intent to be continually nourished by the word of God.  I think verse only suggests that expounding and manifesting of worthiness must take place before confirmation, not necessarily between baptism and confirmation.