To rephrase what Huff360 said, yes you can use a 6 gallon carboy just fine. As long as your are not storing it for a long period of time (>2 months) in secondary you will be fine.
5 gallon carboys are nice to have for long term secondary fermenters, both for less oxidation, and less space needed. 6 gallon carboys are nice to use for fermenting too because they are also glass, so there is less concern about sanitization, and not being oxygen permeable. Lots of people use them for primary fermenting in fact, you just need a blow-off tube (peice of large tubing routed into a bucket of water) because the krausen will rise right out of the carboy, which would block the airlock and cause a huge mess. The carboys are a pain the clean though.
I have 3 carboys and 1 bucket fermenter, which I plan to turn into a bottling bucket this week, and only use glass for fermenting.