Clear immigration at BT, go out and take the free shuttle service to T2, go up to the 2nd level and take the Skytrain to T1.
If your flight lands on time, all this may take you up to 40 mins max and you will still have time to check in for your next flight.
Don't take a taxi as the driver would have queued for some time, and he would not be happy picking up a short-distance fare.
