NOT AT ALL! who said dual hard drive is bad? You can have as many as your computer supports.
RAID 0 does enhance speed, but you shouldn't consider using it unless you really feel you need it and you have some knowledge about it. it has some disadvantages - your drives can't be read on another computer and if one of your drives fails, you lose the data on both your drives. and if you don't have hardware RAID controller, you will experience high CPU usage.
You should be perfectly fine if you don't use RAID.
EDIT: by the way, if you're expecting the Operating System installed in the hard drive from your older computer to work in the newer computer too, it won't. You'll be able to access all the data, of course, but you can't run the operating system from that drive unless you install it again on the new computer.