Brexit is akin to secession, but secessionism is not contagious. Politicians and publics respond most strongly to the domestic political conditions that they live with and provide incentives. If a piece of a federation leaves, then sure, that affects the various actors within that federation. So, secessionism was contagious within Yugoslavia and the Soviet Union. BUT outsiders who are not impacted directly can learn both positive and negative lessons, and they will tend to learn those that reinforce their existing preferences--confirmation base and cognitive closure have a huge impact here.
For example, the Quebec separatists were following the Scottish referendum very closely until the Scots said nay. Then the Quebec separatists basically forgot that the whole thing happened. The lessons Quebec and Canada learned from Montenegro's secession proves the power of confirmation bias.
Quebec separatists: wow, Montenegro had a vote and voila, independent!
Canada: Hey, 55% as a threshold for legitimate referendum.
Quebec: huh? I can't hear you.
To be sure, if the UK leaves the EU, then, yes, Scotland will leave the UK. Things were close enough last time, and the Scots are mostly fans of the EU. What will this mean for Quebec? Not much. Quebec separatism is moribund for a reason. Ok, many reasons: the Quebeckers have gotten most of what they wanted, the Rest of Canada has learned not to poke at the beast by avoiding constitutional discussions, and the Prime Minister happens to be a Quebecker. While that last bit is no guarantee, Quebeckers are less upset with the federation now than they were under Harper, and they were not that mobilized then either. Oh, and it is both a cause and consequence of the weak state of Quebec separatism that the Parti Quebecois is so incredibly lame right now.
There are plenty of good reasons to oppose Brexit,* but spawning separatism in Canada is not one of them.
* My favorites are: massive economic changes that are poorly understood, the magical thinking of the Brexit folks, and, oh yes, that much of the Brexit movement is driven by the same blend of ignorance and xenophobia as the Trump campaign.