Welcome to the community!
Unfortunately, I don't think that would be possible. The plans are associated with phone number and not where you reside. There are often Provincial-specific plans or pricing. If your current plan is specific to British Colombia, it may not be available in Alberta. Even if the plans appear identical, there might be cost differences between the Provinces. If you wished to keep your current plan, you would need to keep your BC phone number.
As mentioned, you would be able to keep your old BC plan and phone numer, though you should note that people from AB calling your phone number might incur long-distance charges. You would also need to verify your plan includes Canada-wide minutes to prevent incurring LD charges yourself. In addition, many building buzz-code systems can only dial local phone numbers (see here).
In addition, you should note that the taxes on plans is also directly associated with phone number (see here).
If you would still like to change your phone number, it's unlikely you will be able to make the change online since you would need to change both your phone number and plan at the same time. You would need to contact customer service. In addition, they can also be contacted via Live Chat, Facebook, or Twitter. Those methods can be accessed via the contact page posted above. There would not be any fee for the change since your move involves a change in local calling area (see here).
Hope this helps 😀