According to the The Hill Times, the Liberals registered the domain name "liberaldemocrats.ca" in December 2008. However, I'd like to point out now that those who run this blog on The Hill times are idiots.
Here is the report:The red circle shows the approval date - essentially the day when it was registered as a domain.
Problem is, there is nothing there noting that the Liberal Party of Canada registered it. In fact, as noted in the blue circle, Netfirms, Inc. itself owns and most likely registered the domain.
Coincidence that it occurred during the coalition crisis, right? No - domain sites like this often go around looking for free sites like this to take over on the basis of what makes the news.
To make a point, a local candidate here in Burlington for city council had to fight for a domain name that had his name in it. They do this in order to make the people who want the domain, pay through the nose for it. It's a way to make money, since domain-squatting is hardly illegal.
Of course, the eponymous Hill Times overlooked this, preferring instead to draw conclusions from nothing. Good journalism right there.