I appreciate your good responses and I'm following up on the references. I have put together a rough time line for the four voyages of the "Julia Ann" from San Francisco to Sydney, based on the records I have been able to find so far.

Voyage #1 Departed San Francisco perhaps in late May or early June, 1853.
        Arrived in Sydney probably in July of 1853.
        Departed Sydney on or about August 25, 1853.
        Arrived in San Francisco on October 9 (or 11), 1853.

Voyage #2 Departed San Francisco on December 2, 1853.
        Arrived in Sydney on January 24, 1854.
        Departed Sydney on March 22, 1854.
        Arrived in San Pedro CA on June 13, 1854. (83 days)
       Arrived in San Francisco shortly thereafter.

Voyage #3 Departed San Francisco for Puget Sound perhaps in early fall, 1854.
       Departed Puget Sound in the fall of 1854. (See p. 102 in the document below.)

http://books.google.com/books?id=KoEUAAAAYAAJ&pg=PA359&lpg=PA359&dq=History+of+Seattle+from+the+earliest+Vol.+1&source=bl&ots=WU
            
        Arrived in Sydney on December 6, 1854.
        Departed Sydney on ?
        Arrived in San Francisco on ?

Final Voyage, #4 Departed San Francisco perhaps in early June of 1855.
        Arrived in Sydney on July 24, 1855.
        Departed from Sydney on Friday, September 7th, 1855.
        Ran aground and sank off the Scilly Islands on October 3-4, 1855.