Yes, as others above have said.
I suggest you initialize your external drive HFS+ (use Disk Utility).
Then, use CarbonCopyCloner (free to download and use for 30 days) to "clone" the contents of your internal drive to the external. (Note: I believe CCC copies _only_ Mac-related files, and cannot clone the Windows partition).
The result should be a bootable external drive that has the exact contents of [the Mac portion of] your internal drive.
CCC can also clone the recovery partition, as well.