There is indeed a QuickBooks for Mac -- however, be warned that Intuit has always treated this product about the same way you might treat a distant cousin who tells rude, non-funny jokes in a loud voice and doesn't bathe regularly -- you'll invite him for Thanksgiving because you have to, but you're going to sit as far away from him as you can manage.
Many of the standard features in QB for Windows either do not exist or are severely limited in QB for Mac. It will look and feel like QB/Windows of several years ago, at best.
However, it does exist, it IS better for a business than Quicken, and it does work just fine within its' limitations. And you can convert from Quicken files to QB files. Pay attention to the changes that have to be made to the Quicken file, and be prepared to try a couple of times before you're satisfied with the conversion (Quicken to QB tends to give some oddball detritus, and sometimes it takes an iteration or two to get a file you're content with). Of course, make a good backup/copy of the Quicken file OFF the conversion computer (CD or flash drive or other, dis-connectable hard drive), so that if something goes awry, you have an uncontaminated data file available for the next attempt.