Do I need to apply for the spouse visa separately after arriving in Canada?

No, you do not need to apply for the spouse visa separately after arriving in Canada. You can submit your spouse's open work permit (dependent visa) application together with your own study permit application before you travel.

Applying together allows your spouse's visa process to run concurrently with yours, making it easier for both of you to arrive at the same time. If you don't apply together, your spouse can still apply from within Canada later, but the process is usually smoother and faster when done simultaneously.