Hi,
Yes, you will need a transistor in the receiver because the phototransistor you specified can only handle 25 mA (and your motor presumably needs more current than that).
In order to time the motor, the easiest way is with a 555. Your phototransistor can be used directly to trigger the timer. Then just hang a transistor on the timer output to turn the motor on and off.
Note that the 555 needs 5V compared to your 3V motor, so you will have to use separate supplies or operate the transistor in its linear mode to keep the motor voltage at an acceptable level.
Regards,
Chris