Terminal size at startup?

Just add geometry to the command with the values you need:

Exec=gnome-terminal --command /home/noah/bin/clock --geometry=24x24

You can see all options with this command

gnome-terminal --help-all

Output:

Usage:
  gnome-terminal [OPTION?] [-- COMMAND ?]

Help Options:
  -h, --help                      Show help options
  --help-all                      Show all help options
  --help-gtk                      Show GTK+ Options
  --help-terminal                 Show terminal options
  --help-window-options           Show per-window options
  --help-terminal-options         Show per-terminal options

GTK+ Options
  --class=CLASS                   Program class as used by the window manager
  --name=NAME                     Program name as used by the window manager
  --gdk-debug=FLAGS               GDK debugging flags to set
  --gdk-no-debug=FLAGS            GDK debugging flags to unset
  --gtk-module=MODULES            Load additional GTK+ modules
  --g-fatal-warnings              Make all warnings fatal
  --gtk-debug=FLAGS               GTK+ debugging flags to set
  --gtk-no-debug=FLAGS            GTK+ debugging flags to unset

Options to open new windows or terminal tabs; more than one of these may be specified:
  --window                        Open a new window containing a tab with the default profile
  --tab                           Open a new tab in the last-opened window with the default profile

Window options; if used before the first --window or --tab argument, sets the default for all windows:
  --show-menubar                  Turn on the menubar
  --hide-menubar                  Turn off the menubar
  --maximize                      Maximize the window
  --full-screen                   Full-screen the window
  --geometry=GEOMETRY             Set the window size; for example: 80x24, or 80x24+200+200 (COLSxROWS+X+Y)
  --role=ROLE                     Set the window role
  --active                        Set the last specified tab as the active one in its window

Terminal options; if used before the first --window or --tab argument, sets the default for all terminals:
  -e, --command                   Execute the argument to this option inside the terminal
  --profile=PROFILE-NAME          Use the given profile instead of the default profile
  -t, --title=TITLE               Set the initial terminal title
  --working-directory=DIRNAME     Set the working directory
  --wait                          Wait until the child exits
  --fd=FD                         Forward file descriptor
  --zoom=ZOOM                     Set the terminal?s zoom factor (1.0 = normal size)

Application Options:
  --load-config=FILE              Load a terminal configuration file
  --preferences                   Show preferences window
  -p, --print-environment         Print environment variables to interact with the terminal
  -v, --verbose                   Increase diagnostic verbosity
  -q, --quiet                     Suppress output
  --display=DISPLAY               X display to use

Select Edit and then Profile Preferences:

Notice 92 columns and 30 rows. You can adjust these values to make terminal larger or smaller. In my case I have it set exactly 1 row less than needed (as I just discovered whilst answering your question):