You probably want to keep track of your transactions in a spreadsheet of your own construction, because unlike in the USA, brokers are not required to keep track of your adjusted cost base for you. You might think you're in the clear because they are showing you an average now, but there's no guarantee that that number on the broker's webpage will be correct in the future.
Just by way of one example, a couple years ago Questrade transitioned to a different trading platform, and in the process, they discarded all historical data on purchase prices in accounts. If you had had Questrade account at that point, your displayed average price would have been reset to the current market price on the date of the transition, completely throwing away the information that you are depending on. Knowing Questrade, that could happen again the future. They are under no obligation to keep that information accurate for you.
Even if Questrade remains accurate indefinitely into the future (an unlikely proposition really), you might transfer the assets to another broker who would not receive your transaction history as part of the transfer.
I would recommend keeping your own records.