Thanks to very detailed research carried out by April Marjoram, the following information has been obtained which identifies Amy Barbaro as Amy Dawson born 1867 in Newcastle upon Tyne.
Here is an extract from the research :
1.Amy Dawson was born Newcastle upon Tyne in 1867 (ref BMD New.U.Tn 2nd quarter 1867 10b/1)
2. Her parents were Edward Dawson (who worked for Newcastle & Gateshead Gas Co) b.1836 and Jane A F Dawson (nee Thompson - see 3.below) Her siblings were (all born NUT): Edward E b.1866; Simpson b.1869 and Edith G b.1874) - in 1871 the family were living at 11 Coburg St Gateshead and in 1881 in Elswick (ref 1871 census RG11/5053/29/14 and ref 1881 census RG11/5051/74/18)
3. Amy Dawson's parents married in 1863 - Edward Dawson married Jane Ann Fredrina Thompson in/around Newcastle upon Tyne (ref BMD 3rd quarter 1863 New.U.Tn 10b/200)
4. 1891 census shows Amy Dawson described as "artist" visiting (or possibly lodging?) at the home of Henry Graham at 16 Bute Street
5. 1st October 1893 Dorothy Worden (who was also born in Newcastle upon Tyne) - a member of St Ives Arts club signed in Amy Dawson from Northumberland
6. 31 March 1901 at 35 Carlton Crescent Southampton at home of Mary Heath widow aged 49 living on own means b. Ireland; Tyrone Power her nephew aged 29 single b India book publisher and Giovanni barbaro aged 37 retired courier b. Italy (Italian subject) and Amy his wife aged 34 b Newcastle Upon Tyne "artist, watercolours" (ref RG13/1060/39/12)
7. 20 April 1901 John Barbaro "artist" aged 34(!!) and his wife Amy "artist"aged 33 left Southampton to sail (2nd class cabin) to New York on the SS New York (ref shipping register)
8. 23 January 1907 Amy Barbaro was one of the two witnesses at the wedding of Dorothy Worden (though by that time she was the widow of William Evelyn Osborn - so is recorded as Dorothy Osborn) to Commander Harold Ernest Browne at St Luke's church, Chelsea (ref P74/LUK/245)
9. Giovanni Barbaro died 1915 whilst his wife Amy Barbaro (ref probate register) died on 20 Feb 1937 at Nursing home (Milton House Strawberry Hill) but here home address was Montpellier House, Montpellier Row Twickenham Effects=£8.8s.2d and probate administration was granted to Gipsy [Edith] Archdale Cook, widow (she had been married to an accountant - see 1911 census ref RG14/6978/127)
10. Amy Barbaro was listed on the electoral register in 1936 at 29 Montpelier Row Twickenham
11. Victorian Painters C.Wood, C.Newall, M.Richarson pub 2008 p133 lists "Dawson, Amy fl1889-1891; exhibited three pictures at SS 1889-91, flowers, fruit and one portrait. London address."
My own conclusion from this information is that, unless it can be proved otherwise, Amy Barbaro was Amy Dawson and she, not as has been previously assumed Giovanni Barbaro, used the pseudonym A. Dudley or Arthur Dudley (maintaining the initials A.D.). She probably adopted this nom de guerre as a male name was preferable to a female name in Art circles in Victorian Britain.