Manage your services:

Margaret, this is one of those age-old time vs. resources questions. Quickbooks is obviously the cheaper option, but it will cost you in time. Vice versa for the accountant, who will be more efficient for you, but cost more. You get the picture.
So, I tend to sort this out with another metric -- by expertise and my needs. If your business is small enough that you don’t need special financial counsel (and you have a little time), go with the software and save the money for marketing or other critical spending. But I’ve found that the right financial partner can help guide me into better business decisions, acting as a de facto CFO. And sometimes they more than pay for themselves by steering you to better business strategy.
One note: Regardless of whether you do it yourself, make sure you have a very firm handle on your company’s finances, especially cash flow. There is no more surefire way to cripple your business than losing track of money.
If you are fairly good at using Quickbooks and have some general accounting experience with debits/credits/balance sheets and the like, it may not be necessary. It may be a good practical idea, though, as a well versed accountant can guide you through your tax year and let you know how to take charge of investing and using your profits and how to do your taxes properly.
If the business is simple enough, you may decide not to have an accountant for the whole year, just have him do your taxes.