I suspect Federation would effectively begin as an Imperial Council with representatives nominated by the colonies and dominions but dominated by the British Government of the day - over time their influence would decrease as more members were admitted and given self-government and critics talked about the democratic deficit of the Imperial institutions. (AKA the European Union)
Here's a very rough idea of how it might be achieved in the 1890s - after WW1 i think it would be very difficult to achieve due to rising nationalism in the principal dominions and the huge war costs Britain was saddled with.
Assuming its passed in say 1892.
The Act of Parliament required would have probably essentially allowed colonial governance in terms of expansion, defence, development, expenditure and trade to rest with an Imperial Council whilst national parliaments, commissioners and governors retained domestic responsibilities for their nations.
Westminster would probably insist on retaining an Imperial veto effectively meaning that any decisions made by the Imperial Council could be overridden by the Westminster Parliament. Arguments would have included the fact that an unelected body should not have the power or authority to force the country to war or to amend taxation and trade policy without reference to Her Majesty's Government. The Imperial Council's decisions would require ratification by national parliaments in some circumstances.
Rights reserved from the council to the British Government would also include matters relating to the Royal succession and title.
Pro-federalists had long believed this to be a way to ensure the Empire's survival without having a complicated elected Parliament with a very diverse population base. It also satisfied British concerns over the home nations being dominated by some of the larger colonies in particular India with its vast population. It also meant that the larger colonies in particular Australia and Canada had a say over Imperial policy.
The Imperial Council as constituted in 1892:
Non-Voting members:
Lord President of the Imperial Council - appointed by Her Majesty on the advice of the British Government - often a high-ranking aristocrat or member of the Royal Family.
Advisory members (non-voting and in practice rarely attended but had the right of consultation over policy though they had no veto)
The Governor Generals of all the Dominions (or their appointees)
The Secretary of State for Colonial Affairs (or his appointee)
The Viceroy of India (or his appointee)
The Secretary of State for India
Members (with voting rights)
Chairman of the Council - the Prime Minister of Great Britain and Ireland.
Treasurer of the Council - the Chancellor of the Exchequer
The Colony of New Zealand - 2 members nominated by the Parliament of New Zealand
Australia - 6 members (1from each of the six British Colonies)
The Dominion of Canada - 4 members
Newfoundland colony - 2 members
The Cape of Good Hope colony - 2 members
Natal colony - 2 members
The United Kingdom of Great Britain - 6
Voting members: 26
In 1896 the Imperial Council proposed the admission of new voting members for those colonies and protectorates who did not have a voice on the Council. This would include Britain's Caribbean colonies, British South America its possessions in the Med, Africa and the Indian Ocean etc.
It would have also included stronger representation from India.
The British Government largely was unmoved by the idea but eventually a compromise was reached in that the new members would largely be nominated by the Colonial Office and advice of British Commissioners, Colonial Governors and other interested parties.
The new members were split into the following groupings:
West Indies and the Caribbean - 2 members
British Guiana - 1 member
The British African Colonies and Protectorates - 2 members
Other British Crown Possessions and Protectorates - 2 members
India - 4 members (all of whom were members of the Council of India)
Total voting members: 33
All members of the Imperial Council were entitled to add IC (Imperial Councillor) after their names in a similar way to that of Privy Councillors.
The decision by the Government to nominate representatives from many of its younger smaller colonies and protectorates predictably ensured the UK had a strong voice on the council effectively allowing it to lead policy. It became a significant source of tension between the older Dominions and Britain over time.However the tenure of councillors of four years and changing political situations in their own countries did not always guarantee the council would be merely a tool of the British Government and often councillors would over time show considerable independence of thought.
India's representation had been problematic given her size, Queen Victoria's reluctance to see any organ of state dictate to the Indian Prince's and her own belief in her role as Empress of India. It was eventually agreed the Viceroy would have a non-voting advisory role and in 1896 four members of the Council of India were appointed to the Imperial Council co-nominated by the Viceroy and the Sec of State for India.
Attempts by the Imperial Council to grant Dominion status to India were tried in 1903 and 1905 but were defeated, a vote did pass in 1909 however was vetoed by the British Parliament by a narrow majority.
Changes to membership were made following the Boer crisis and the creation of the Federation of Australia. Further changes were made following the creation of the Union of South Africa.