Technically a payslip of your wife is sufficient. But I think you should include your payslip, too, especially if you wife's income may be considered to small to support you both.

Most likely they will ask for recent payslips anyway when they actually get to processing your application. My understanding of the system is that your application is sitting in a queue for a few months, because the Home Office is too busy to process it straight away. If you include an EEA1 application for your wife in the same letter, both may get processed a bit faster.

Tom