If we assume things go pretty much as OTL untill 1864, then Cape Breton will almost certainly be interested in a Maritime Union and have representatives at the Charolettown conference. This conference was schedualed to discus a union of the Atlantic Provinces untill a delegation from the United Provice of Canada crashed the party. How the negociation might change with an extra party I don't know.
But for the sake of argument let's asume that an agreement not unlike OTL is reached whereby New Brunswick, Nova Scotia, Ontario, and Quebec all become provinces of Canada in 1867.
In OTL the new government had to make promises of expensive transportation links to bring in the holdouts of British Columbia (Canadian Pacific Railway) and Prince Edward Island (ferry service to eventually replaced with a brige).
What did Cape Bretoners' need built that they could haggle for from Ottawa? When was the Canso causway built? Perhaps they would get a brige instead? Or the CPR diverted to Sydney which become an important port?
As for Dominion status. That's almost out of the question because I would think Britain would be leaning on Cap Bretoners hard to join Canada.
Some other questions: Would Scots Gaelic or French have special status in the province? How many Senate seats would CBI get? What city would be capital?
Good POD BTW.
-ch