We'll have you hooked on this internet business in no time!

It seems she may have used the name Letitia overall....?
You say she left Liverpool 23 Dec 1861......
Is this her arrival?
http://proarchives.imagineering.com.au/index_search.asp?searchid=23RILY, LETITIA age 20, Mar 1862 on Star of India
Port B, Fische 201, page 003
On the same ship, month and reference is:
RILY, ANN age 22
Possibly a sister....?
Also on same ship, month and ref was:
REILLY JEMIMA age 19
I wonder if your ALice Letitia embarked on ship in Liverpool, or perhaps in Ireland before the ship went on to Liverpool to pick up more passengers? If she did embark in Liverpool though, perhaps she may be found in the 1861 Census for England......
Cheers
AMBLY