I can't reply in depth for Canada but Australia didn't federate until 1901 - well over a century after American independence. At the time of US independence Australia was not settled (and in fact one of the reasons for its early growth was the loss of the 13 colonies). From early settlement in 1788 by the first fleet until 1825 all settlement was managed by a british appointed governor who resided in Sydney. From 1825 NSW and Tasmania (Then known as Van Diemens Land Colony) formally split and from there there was only a growth of independently run colonies which eventually grew to include Victoria, Queensland, South and Western Australia. Ithink this shows that the Bristish never had a united Australia as goal as from the outset they granted new independent colonies.

In fact before Australia federated it was never certain that all colonies would consent to federation - for some time it looked as if Western Australia would stay a seperate colony although once the results of a referendum on joining came in it was clear that it would too.

In any case this process and drive for federation for a united Australia was driven by internally by Sir Henry Parkes - it was never an externally imposed amalgamation.

As an aside, a funny and little know fact is that New Zealand was invited to join the new proposed Australian Federation and sent representatives to the early Australasian Conferences but as there was not popular support for the motion evwntually declined to join.

So to wrap up I would say that the British never had designs on uniting Australia and in fact allowed the growth of independent colonies from after American Independemce. From what little I know of the Canadian confederatio, I suspect you'll find that this holds true for Canada in the late 18th century. Confederation in any case happend well after the war of independence.