It sounds like you want to have your original table open, and a transpose table beside it, then when you type new data into rows (or columns) in your original table it just appears as new columns (or rows) in the transpose table. Correct?
I don't believe there is a way to do this in JMP. Transpose is an operation on a table that creates a new table. If you want a transposed table with your new data included, you would need to transpose your table after it has been added. (If you are doing this regularly, you could add a script to your table and possibly make it easier for yourself.)