How to separate commands issued in a terminal from their output?

I'm realising that for 90% of my day I'm staring at the same part of my screen -- the bottom-left corner -- while I type commands and wait for output. I'm starting to develop quite the neck strain, constantly staring downward like that and it got me thinking: surely there's a way for my terminal to separate the line on which I'm writing commands from the output that they generate, and therefore place the input line consistently at the top of the screen?

Something like this:

+---------------------------------------------+
| $                                                                           |
+---------------------------------------------+
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
+---------------------------------------------+

⬇

+---------------------------------------------+
| $ uname -om                                                                 |
+---------------------------------------------+
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
+---------------------------------------------+

⬇

+---------------------------------------------+
| $ echo "Hello World"                                                        |
+---------------------------------------------+
| $ uname -om                                                                 |
| x86_64 GNU/Linux                                                            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
+---------------------------------------------+

⬇

+---------------------------------------------+
| $                                                                           |
+---------------------------------------------+
| $ uname -om                                                                 |
| x86_64 GNU/Linux                                                            |
| $ echo "Hello World"                                                        |
| "Hello World"                                                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
+---------------------------------------------+

Is this something that can be done with a creative Bash prompt, or maybe with tmux or something else like a GTK terminal emulator I've not heard of yet?