You are not automating the process too much as the script is still querying the user for her password...

You can do the same with just some shell lines:

$hosts ="host1 host2 host3"

# use ssh-keyscan to populate your "known_hosts" file first:
ssh-keyscan $hosts >>~/.ssh/known_hosts

# then append your key on the remote hosts:
for h in $hosts
do
  echo "*** copying key to $h ***"
  cat ~/.ssh/id_rsa.pub | ssh $h 'cat >>~/.authorized_hosts'
done
[download]

update: read also ssh-copy-id man page!