There's no direct way to get the progress of your rsync command - once AppleScript calls the do shell script command it has no visibility into what that command is doing until it's finished.
There is one workaroud, but it takes some effort. You can execute the shell command in the background - this passes control back to your AppleScript while the shell command is still running. In addition, you can redirect the output of the shell command to a file and your AppleScript can read that file to determine the progress of the command. It's not trivial to do, but it's about the only option you have.
-- run the command
set thePID to do shell script "/path/to/lengthy/process &> /var/tmp/my.out & echo $!"
-- grab its ID
set processIsRunning to true
-- repeat while it's running
repeat until processIsRunning is false
tell application "System Events"
-- if this works, the process is still running
do shell script "ps -p " & thePID
-- so grab the last line of the output file
set progress to last paragraph of (read POSIX file "/private/var/tmp/my.out")
-- if we get here the process isn't running, so clean up
set processIsRunning to false
do shell script "rm /var/tmp/my.out"
-- show the output
display dialog progress