In answer to the OP, yes, title to Crown lands that have been registered under the provincial titles system is in the name of “Her Majesty the Queen in right of [name of province or Canada],” depending on which government owns it. So, if you buy registered Crown land in say, Ontario, the transfer will likely read “From her Majesty the Queen in right of Ontario to Sunspace.”
But, you have to remember, as Monty so succinctly pointed out, that there is a difference between the Queen in her personal capacity, and the Queen as the Crown, formal head of the executive for Canada or a province.
If the Queen owns land in her personal capacity, bought with her own money, it is not “Crown land,” and it is not subject to political control. She can sell it or lease it just like any other land-holder.
On the other hand, if land is Crown land, owned by the Queen in right of a particular government, it is public land and can only be alienated pursuant to the laws of that government. The Queen would not be personally consulted, and would not have any say in the disposition of the land. Typically, a sale of Crown land requires an Order-in-Council (i.e. - an order of the provincial/federal cabinet), signed by the Minsiter responsible, counter-signed by the PM, and approved by the Lieutenant Governor/GG in the name of the Queen.
The other issue that has been discussed on this thread confuses the issue of property with sovereignty.
A nation is sovereign over its territory, but that does not mean the nation owns all the land civilly (except in the late unlamented USSR, Cuba, etc.). So, if you buy a piece of Crown land from the Queen in right of Canada, that does not mean it ceases to be part of Canada - merely that private ownership has passed.
On the other hand, at international law, a nation can cede sovereignty over a territory to another nation on whatever terms it sees fit. One common reason for cession is that it has lost control of the territory by military action (e.g. - Treaty of Paris, 1783 - U.K. ceded sovereignty over the 13 colonies).
But, a nation can also cede sovereignty for cold hard cash, and that is what happened when France decided to cede sovereignty over the Louisiana territory to the U.S.
However, in modern times, such a cession is highly unlikely without extensive political consultation, such as a plebescite amongst the inhabitants.
Finally, to end a long post, a short anecdote. About 11 years ago, there was a rumour floating about in New York that Princess Di was breaking up with Prince Chas. (they got that right), and was moving to N.Y. The rumour also said that the Queen supported the move, and had bought Di a condo in N.Y
Turned out that the rumour started because the Canadian goverment had bought a condo for one of its U.N. diplomats, and the title issued by the N.Y. titles office listed the owner as “Her Majesty the Queen in right of Canada.”