I haven't taken the Peachtree course yet, but I guess it depends on how much time you study per day on how quickly you get through it. As for Quickbooks that doesn't take long at all. As a matter of fact I believe you have to finish the course within 30 days because the Quickbooks software is trial software that expires in 30 days.
Having a previous degree will certainly help. It's more points in your favor than someone who has no degree; however, that said your degree is in math and not accounting. Bare in mind you're going for accounting clerk jobs (generally what they call bookkeepers in the want ads) not an accountant. If you find you really like bookkeeping and want to progress to an accountant you can always consider going back to school for accounting. There are a lot of options on how to get the education necessary. Assuming you have a bachelor's you could take the prerequisite courses and the do a master's in accounting, or take 150 total credit hours of undergraduate credit (including what you already have) with 30 credit hours in accounting to sit for the C.P.A. exam. Although requirements very from state to state, what I have just stated has been adopted in most states for the C.P.A. exam. If that becomes something you're interested in check you state board of accountancy. Call Penn Foster student services and ask if you can take the Peachtree course as a stand alone course.