In a speech in London, the Scottish Labour leader said the opposition should convene a People's Constitutional Convention to reach a new devolution settlement for the whole UK.
Ms Dugdale warned that the fallout from the EU referendum "risks breaking the Union once and for all", with the Scottish Government seeking independence in Europe while UK ministers push ahead with Brexit despite Scotland's vote to remain.
She said Scotland had been "the canary down the mine" during the independence referendum and said "politics driven by nationalism and identity... have now taken their place firmly in the mainstream of all UK politics."
Ms Dugdale said: "The time has come for the rest of the UK to follow where Scotland led in the 1980s and 1990s and establish a People’s Constitutional Convention to re-establish the UK for a new age.“The convention should bring together groups to deliberate on the future of our country and propose a way forward that strengthens the UK and establishes a new political settlement for the whole of our country.“Some may say this is unrealistic, but it would follow the model of the Scottish Constitutional Convention which, without Government support, established the basis for the settlement that delivered a Scottish Parliament in 1999. “It would also – for the first time – provide a coherent approach to answering the question of how our country is best governed.She added: “While devolution has been positive for Scotland, Wales and Northern Ireland, we have to acknowledge that progress has been erratic and while there has been significant progress in some parts of the UK, other parts have been left behind."“So I would not want the convention to just deliberate and report, but to produce a new Act of Union which would reaffirm the partnership between our nations and renew it for the future.“After more than 300 years, it is time for a new Act of Union to safeguard our family of nations for generations to come.”
Ms Dugdale said the convention should set out the case for a "radical reshaping of our country along federal lines" resulting in "significant changes to how central government operates".
She reiterated calls for the House of Lords to be replaced with a "Senate of Nations and Regions" sitting outside of London, and said social protections including workplace rights should be devolved once they return from Brussels after Brexit. Ms Dugdale also said Scotland should set its own minimum wage.
However, she said the UK would continue to have an important role in guaranteeing the "safety net of social protection" and redistributing wealth.
Proposals for an new Act of Union will be put to the Scottish Labour Party conference at Perth in February.
Ms Dugdale said the plans had been discussed with UK Labour leader Jeremy Corbyn.
The Scottish Labour leader said the case for Scottish independence was weaker after Brexit, claiming it would erect trade barriers with the rest of the UK in an "act of economic vandalism far greater than even Tory Brexit has handed us."