Q:

How do I successfully create the Imperial Federation?

I know it sounds like something out of a Star Trek film, but the Imperial Federation truly was an existing plan. Proposed in the later half of the 19th century, the plan was to incorporate the British colonies, including the largely self governing ones like Canada and Australia, into Britain itself. 
The proposal was to create a single federal state among all colonies of the British Empire. The federation would have a common parliament and would be governed as a superstate. Thus, Imperial unity could be maintained while still allowing for democratic government. The colonies would increase their influence while Britain would be able to share the costs of imperial defence. The best features of large states could be combined with the best features of small states.
It was seen as a method of solving the Home Rule problem in Ireland, as England, Scotland, Wales, and Ireland (along with the other members of the Old Commonwealth) would have their own Parliaments.
There were two main obstacles of this plan, the first being the vast distances between this lands. Though Edward Ellis Morris pointed out that it was now as easy to reach London from Melbourne as it had been to reach London from Orkney at the time of the Acts of Union 1707, or to reach Washington, D.C. from California before passes over the Rockies were made.
Another obstacle to the scheme was what one of its proponents, Richard Jebb, called colonial nationalism. The granting of authority to a super-parliament composed of many competing interests was seen by opponents as a compromise to the powers of the local parliaments. Leading colonial supporters of imperial federation, such as Australian prime minister Alfred Deakin, however saw the movement as a way to increase the influence of the dominions over imperial defense and foreign policy. The colonial branches of the Imperial Federation League in fact outlived the demise of the home branch in London, which collapsed in 1896 when it failed to resolve internal disputes over imperial trade policy.
Then World War 1 occurred and all hopes for the movements died out with it. What is the smallest change that can be made in history to allow for the Imperial Federation to exist? 

A:

The biggest obstacle to success here is not so much speed-of-communication, or even colony-nationalism.  These issues can be dealt with.  Communications improve over time, and by the time-frame you are interested in, should suffice given a federal enough structure.  Colony-nationalism (sez I) grows from not having enough skin in the game with respect to decision-making.  Resentment grows if the colonies feel like they're not in the loop on making decisions.
This is where that "biggest obstacle" comes in... historically Britain has been very leery of letting colonies or colonials in on the decision-making loop.  This was a major part of the buildup to the American Revolution.  The British government (a) enjoyed taxing colonies because it was fun ;D, and (b) was rightfully worried that the colonies' population would eventually outstrip that of the Home Isles, and essentially "take over" by weight of having more representation.
So ...
If you want a more integral Empire, you need to overcome the Home Island guys' fear that any Empire representative enough to make the overseas folks happy would end up "wagging the dog" for Britain.
This effect is magnified in non-settler colonies, where the inhabitants are not exactly descended from Britons, and have different cultures.  (Imagine if India were to have proportional weight in Parliament and the very next day had a majority and started changing all the bank holidays to Dewali...)  
So, what can we do about this?  Some ideas...
The Boring Way
Let's posit that someone in the Home Isles starts a "One People, One Empire" movement specifically aimed at making Britons feel more connected to the Anglo-settled parts of the Empire and vice-versa.  This upswell of sentiment influences Parliament enough to make them bend on representation from Anglo-cultured areas.  To assuage their fears, the House of Lords -- there aren't a lot of Lords in Australia, mind -- seizes more powers, so that the Home Isles do have more sway than their population allows for.  The "Far Shires", as the overseas lands with representation are called, are mollified enough by the concessions they've gotten that they can go along with it, albeit with some good-natured grumbling.  
Just to really drive it home, that "Someone" in the Home Isles will be the Crown Prince, who falls in love with a nice South African girl and has the epiphany.
After this system settles in for a while, some of the realms in India want a piece of the action.  Local elites feel that they're sons and daughters of two cultures, and want in.  "We play cricket for fuck's sake.  How much more Britannic do we have to be?"  This is the main issue of the 20th Century.
The Fun Way
Napoleon's forces manage to distract the British Navy and land armies in England proper.  Swift courier ships manage to escape.  When the overseas possessions hear of this, they independently mount relief expeditions -- primarily South Africa, Australia, parts of India all send men.  They meet up in Ireland (and are quite surprised to see one another) and counter-invade.  This hastily organized force flails around the Midlands fighting random French detachments, until the return of the Navy strands all French forces, preventing any reinforcement, and necessitating their eventual surrender.
This display of heart from the overseas groups didn't have a huge effect on the war in truth, but the moral impact was thunderous.  It becomes unthinkable to not take the colonies into account, and the Empire grows together instead of apart.
The AWESOME way
A freak meteor shower throws up a shroud of dust over the northern latitudes of the Northern Hemisphere, making agriculture impossible for a number of years.  Desperate and starving, the population is moved en masse to South Africa, India, Australia.  The Angrezi Raj is born!  Thank you S.M. Stirling!

