I don't think you need to show you are making $1K/week in order to have your visitor visa extended. But I believe CIC looks into how much money your b/f makes a year in order for them to see if he can financially support you while living with him. If you say that he doesn't have a steady income, instead of showing a bank statement in the last 3-4 months, have some sort of bank report showing the income in the last year. If you have any saving account you can show them the statement from that as well.
We asked for one year extension last year, and luckily we got it. We wrote a letter explaining that we intend to apply for sponsorship, we attached upfront medicals that we did last year, police certificates, bank account statements, my letter as a sponsor stating that I will cover all financial needs while he is Canada with me. This weekend we are going to apply for another extension, and we hope we'll get it. We will ask only for 6 months this time. And even though we just sent the application package and don't have an AOR or other hard evidence, we will show them the proof proof that our application was sent and was received in Mississauga, we would like to be together until we receive the PR.
What I would do if I were you is visit your b/f for 6 months (if you are not in Canada already), after 5-5.5 months of being in Canada apply for a 6 month extension telling CIC that you would like to be together in order to be living with him continuously for one year (you would still need some bank statement of proof of income from your b/f to show he's being able he can support you. Or have some bank statement on your name as well, or have a letter from you parents stating that they will send you money to help you while on this "journey"). Once you get approved for another 6 months, start preparing your application. Before the second 6 months end, do your upfront medicals (at this time you should be at around 11 months from that 1 year you need to be together), get any police certificates or FBI clearance if you need to, pay the $1040 process fee. Then send a letter to CIC asking for another 6 months showing them all the proofs that you are indeed preparing to apply for sponsorship/PR. You would still need to show again some proof of income. Even though sponsoring a spouse/common law doesn't require having a mandatory yearly income, showing that he is making enough money to support both of you helps.
All the best, and I hope you will get your extension.