I thought I'd have a look through some records for you. You may have the information you require by now, but here goes.
I could not find Alice Walsh on the 1871 Census. I noticed on the Ancestry website that one of the family trees has her listed as being born in St Joseph's Parish, Guernsey, but there is no such Parish.
Later Censuses confirm that she was born in St Peter Port Guernsey - there is though a Catholic Church in St Peter Port known as St Joseph's, so maybe she was Baptised there? Especially with her mother being Irish (Just a thought!)
Was Catherine Walsh the daughter of Patrick and Mary Walsh? They appear on the 1871 Census in St Peter Port Guernsey, but no trace of Catherine's daughter Alice with them.
1881 Census and Alice is living at 9 Hue St, St Helier Jersey. Her birth year is given as 1870 Guernsey. She is a Scholar residing in a Boarding House (Boarding House owner Jane Alexandre)
1891 and 1901 Censuses, Alice M Harben living with her husband Thomas E Harben, the Seafaring Man in St Helier Jersey (no children).
Thomas Harben made a Will on 25/2/1905 in St Helier Jersey (this information from Jersey Heritage Archives)
Thomas Harben is listed as having Died 25/11/1909 in St Helier Jersey (per Ancestry website)
1911 Census, Alice still living in St Helier Jersey, she is a Widow and her name is Alice M Harben. Census confirms she was born in St Peter Port Guernsey and the place name of her father is given as Ireland (maybe this is just referring to Catherine? as her father was Guernsey born). Census also confirms that there were no children from her marriage.
Her occupation is given as Boarding House Owner and her address as St Lukes Lodge, Elizabeth Street, St Saviours, Jersey.
She would have married John Winter Nicolle after 1911, so it must be another Alice who married a J W Nicolle and moved to England before 1909.
There was a John Winter Nicolle who had been born in St Helier Jersey in 1873, who was still single at the time of the 1911 Census and living in St Saviours Jersey (same Parish as Alice M Harben nee Walsh)
I think he's most likely to be the right one.
The other J W Nicolle that I found on the 1911 Census was born in Guernsey in 1869 and married to an Alice (nee Nicholls) who had also been born in Guernsey in 1869, but they had been married for 23 years by this time (1888) and had lots of children (Grace, Florence, John, Percy and Henry born in Guernsey (up to 1899) and George and Lillian born in Plymouth Devon in 1901 and 1908.
He was in fact a J T Nicolle, but some transcripts appear almost as a J W Nicolle.
This one does not fit with Alice being married to Thomas Harben, so can be ruled out I believe.
Hope that helps.