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Looks like Scots Gaelic. Googling gets an obituary for a 91-yr-old Dollag from the Outer Hebrides - so it's been around for at least 91 years - and this link to a TV programme on BBC Alba:
http://www.bbc.co.uk/programmes/b007hxc8
seems to translate it as 'doll' The 'ag' part seems to indicate a diminutive, like Morag, so I'm guessing it's a Scots Gaelic form of Dolly. Could be wrong though.:)

Well, it's female since she's the grandmother and the family was from Scotland. No other info unfortunately.