I believe they will look at year end income, if you make some one week, you may lose it the next. At the end of the year you should get a statement from your online broker saying whether you made money or not.
Since you can't be on EI for the whole year, I don't think they will go through every transaction to see what week you traded, although with CRA, you never know. If you make a profit you will have to pay tax on that. This is just my opinion.
You can call EI and CRA and ask them, they won't know who it is, I've done it many times for different queries, they don't mind answering anonymous questions, at least when I called them anyway. I'm sure this situation has come up before.
I believe it's considered other income.