You can apply together or separately for PR depending on the number of points in each case. But if only one applies for PR, then the other is not eligible to work because it is considered non-accompanying spouse. So basically, if you both want to work and live in Canada, then you will both need to apply for PR.
The other alternative is to apply for work permits:
http://www.cic.gc.ca/english/helpcentre/answer.asp?qnum=199&top=17