no - extending your stay as a visitor for US applicants does not mean she needs a visa. she will enter as normally, then apply for the extension when necessary. She can ask for 12 months, and say it is to be able to gain commonlaw for pr status. Extensions are rarely denied for US visitors, though you may not always get the amount of time requested.
Yes, if she needs to, she can then apply for a 2nd extension to help get through the PR process. If she's in canada as a visitor, she can still send in an OUTLAND application for PR. She does NOT have to be in the US to apply outland. IF you don't want to wait the full 365 days to become commonlaw, the other option is to get married.
Your girlfriend definitely does not want to try to cross the border with all of her worldly posessions, as she will be turned away immediately. She must remember she is NOT "moving" to canada, she is coming to "visit" her boyfriend. Since she is not married, border agents will be concerned about her being able to prove ties to the US so they know she will return when she says she will. At this initial time of crossing, don't mention intentions to extend the stay. She is there as a visitor only. She will not be able to legally work or study a program that is longer than 6 mo. in lenght.