Hi @AllenJH,
You can copy the column headers by selecting the columns in the columns list on the left, and then copying with Edit > Copy As Text (not Edit > Copy). Then, select the first row and then Edit > Paste.
In JMP 16 (available 2021) there are built-in utilities for situations like this available under Cols > Column Names >. For earlier versions of JMP, I highly recommend @MikeD_Anderson 'sColumn Name Utilities II Add-In, which adds these same utilities.
So why not Edit > Copy? Edit > Copy returns text in rows, which is useful when you're copying column names from one table to another. Edit > Copy As Text will return a tab delimited list, which is good for this particular case where what you are asking jmp for is the transpose of your columns list.
Result from Edit > Copy
5.1
3.5
1.4
0.2
setosa
Result from Edit > Copy As Text
5.1 3.5 1.4 0.2 setosa
I hope this helps!
@julian