I did exactly what you're trying to do recently using CCC 3.4.3 with no issues. I'd advise against using the beta as well. No reason for it really. 3.4.3 works with Lion.
CCC's standard file-level copy will create a bootable copy of your Mac's main partition, but it will leave behind the Recovery partition.
If you're worried about that, you can get CCC to do a block level copy instead of a file-level copy, which will preserve the recovery partition. This requires the new drive to be slightly larger than the original, and it also requires that you're running CCC from neither of the drives you're trying to clone.
My approach was to do a fresh install of Lion onto a 16GB USB drive. 8GB might work, and I like having a bootable USB version handy anyway. I then booted my machine from this USB drive, downloaded and installed CCC and started the block level copy from my internal drive to the new one in a FW800 enclosure.
The result was an exact duplicate of my old drive, but with more space. Booted up perfectly. You can read more about the block level copy feature here.
PS: According to this FAQ, you could just do the file-level copy of the main partition, then recreate the recovery partition after the fact using the Lion Recovery Disk Assistant. So that might be worth a shot too.