You could use sed as follows I think:
- save the first line into the
holdspace - prepend an extra tab (column) from line #2 onward (this preserves the original column alignment of the header)
- at a specified following line (I used line #4 in the example below), swap the
holdback intopatternspace, strip whitespace from it, and prepend it to the line
$ sed -e '1h' -e '2,$s/.*^/\t&\t/' -e '4{x;s/[[:space:]]//g;G;s/\n//}' file
CAT
DOG DOG DOG DOG DOG DOG DOG
DOG DOG DOG DOG DOG DOG DOG
CAT DOG DOG DOG DOG DOG DOG DOG
DOG DOG DOG DOG DOG DOG DOG