What visa do you currently have now? If you have a work visa and then apply for a spousal visa, there shouldn't be any issues working during the "processing" phase. However if you have no visa, then you'd be visa-less until the spousal visa came through and be unable to work.
As for processing time, I believe Immigration says it can take anywhere from 1-3 months. Looking at the flag in your profile my guess is that it will not take too long (2-4 weeks maybe?). Just be sure to have all the paperwork requested and all the documentation spotless.