You will need a pre-1900 POD. By 1910, Canada, Australia, and NZ are dominions. By 1919, Canada banned Canadians from accepting Royal titles, and by 1942 Australia was issuing military orders that conflicted with the British orders. They have separate governments and militaries but generally follow the UK foreign policy. Using the same standards for "dominion", the UK is currently a "dominion" of the United States and a part of the USA empire.
For a POD, you need to go a few decades farther back and restructure the British empire. At various times in the 1800's, the British looked at creating an Irish parliament to handle domestic affairs and to allow the British Parliament to handle "national" affairs. The sticking point surprisingly was not the autonomy for the Irish, but the question of an English Parliament. Also creating an English Parliament in addition to an Irish Parliament is effectively demoting England to just one of the many states of the British Empire, and involves a huge loss of power and prestige for many in England. In the next paragraph, i will give a POD, to illustrate why it so hard to do, not as a POD with any real likelyhood.
In 1840, King George and hugely popular PM Blackstone decided they want the British Empire to last a 1000 years like the Romans did, and begin a review of History. From the American revolution, they see many tactical failures, but not that George Washington really wanted to be a commission major in the British Army and minor nobility. Likewise, a majority of power brokers in the colonies could have been co-opted with power and rank. They also note that Rome had emperors from outside of Italy, and Britain needs a system where members of the dominion can be the leaders of the empire. They key to a lasting empire is for Canadians to think of themselves as British who happen to live in Canada, not Canadians whose country happens to be in the British Imperial system.
The first order of business is to create the parliament of England that has the same status as the parliament of Canada, NZ, etc. The powers of these "state" parliaments will need to be clearly defined. This part is fairly easy, except for the demotion of status for England. Now the House of Commons needs to be reconstituted. One-man, One-vote, for all white males in England, Scotland, Wales, Ireland, Canada, Australia, NZ, South Africa, and whatever other areas you want in the empire today. Now the British Isles are a probably a minority of seats now, and England is a minority. So now, we would expect to see a good number of non-England PM and cabinet people.
Now to the house of lords. Back then, they have real power and they are dominated by titles of England. There are about 1600 or so peers. We need something that is more fair and proportional. So we demote all the lords below duke to their "state" house, so English baron is now a member of the House of English Lords. The Dukes remain in the house of Lords, and there are about 68 of them, and there are more subjects outside the Island as inside. Appointing 30 dukes from the Dominions in the first year and 1 Dominion Duke per year for 50 years will balance it out enough. King George is ok with this.
This process has gutted the English power structure, and is still not totally fair when viewed from dominion perspective. And there is more that has to be done. Affirmative action for flag ranked officers. Affirmative action for the colonial office so aspiring Canadians have a far shot at making Viceroy of India. Building a new capital for the new "Empire Government" makes sense, to show that there is a new start. But where? Are French Canadians and Boers fully franchised in this system?
The above is not a realistic timeline, but tries to show how big a mental step it would have been to truly make the dominions a integrated part of the British Empire, the way Texas is a part of the USA or Gaul become a part of the Roman Empire.
Now if one looks past how radically different the world would be, yes, a surviving British Empire would still be a great power with a focus on Naval Power. Canada, Australia, and NZ would be enough for this power status, but i think the stronger Empire would have retained additional territory for strategic reasons.
1) Singapore - Such a valuable location, and once racial issues are lesser in the 20th century, why not have also make them full citizens. Maybe even try to keep some of the oil fields in the area.
2) At least part of South Africa. So many mineral resources.
3) Hong Kong - The empire would want, but China still wants back badly. But maybe enough butterflies that China accepts.
4) Suez Canal - Tried to keep anyway, stronger empire is likely successful.
5) Small strategic islands such as Zanzibar, Jamaica, Bahamas, etc. Not all, but some likely butterfly into the empire.