If you can remember your password for logging in here you're good to go.
If you can't, then log out of the game on your phone, then go back to login, click sign in, then follow the recover password process. If you don't appear to receive your password email, then check your spam/junk folders.
You are allowed to play the same account on more than one device, just install the game on your laptop and use your normal login name and password.