Here is my timeline I have made for this alternate timeline.
Year 1700 AD
During this time Britian colonizes Brazil , encountering South American natives and subjugating them one by one meanwhile slaves bought from Africa are bought to the colony to be used for slave labor in exporting sugar , canes and other valuable resources to bring to the motherland .
Year 1775 AD
The British colonize more of the Brazilian coast leading to more natives being subjugated and dying of illness bought by British Settlers and their slaves meanwhile during this time the empire is rapidly advancing due to slave labor rapidly producing sugar , cane and cotton as well as slavery in the 13 colonies and caribbean contributing to cotton and sugar production .
Year 1776 AD
The US eventually gains independence however Britian is not much effected still carrying a big monopoly on land and still having vast resources in sugar production in the up coming years it would remian an important colony to combat the Spanish and Dutch in South America.
Year 1900 AD
With tensions in Europe rising Brazil remains a British colony however much like Canada , Australia and New Zealand it became a self governing dominion helping Britian with trade and with wars but still having a somewhat self dependent government .
Year 1920
By The End of WW1 , The British Colonies in America and Oceania begin to ask for independence and start gaining more freedom including Brazil , Brazil helps the British Empire during WW1 and WW2 contributing soldiers to fight against Japan , Italy and Germany alongside Canada , New Zealand and India.
Year 1945-Present
Eventually as WW2 comes to a close , Brazil as well as most of the other British Colonies gain independence becoming fully independent but still staying part of the British Commonwealth and keeping the British Queen as their head of state , Brazil is currently a first world nation in this timeline with standards of living and politics much like Canada or New Zealand remaining as one of the only South American nations with good quality of living .
Brazil aids Britian when Argentina attacks the Falkland Islands in 1982 thus leading to a even more conclusive defeat for the Argentines and insuring British rule on the Island due to Argentina now being surrounded by two enemies willing to defend the island.
Brazil would likely have a similar GDP and Economy to what it has today meaning it would likely be richer than Canada but still way below the US but providing the British develop it like how they developed Canada or New Zealand then it would be a growing economy and a regional power in South America.
If anyone is wondering I think that Guyana would be part of Brazil in this timeline and I also think that it is possible for the British to snatch Suriname from the Dutch and add it as part of the British Brazilian colony .
Also Sri Lanka , Singapore , Malaysia and the United Arab emirates would get independence like they did originally but I accidently marked them in red so my error on that.
Some other things I would like to add
Capital:Saint Luther
Ethnic Demographics
61.9% White
29% Black
7% Asian (Indian/Pakistani , East Asian , Middle Eastern and Southeast Asian)
0.9% to 1% Native Brazilian
0.1% pacific islander/Latin American/other
Land Area:3.33 Million Square Miles
GDP:1.899 Trillion