Perhaps you should consider a point and click game. Or you could even try a non-violent FPS puzzle game. For instance, rather than shooting creatures, you have to pick a sonic screw driver mode, and point it at locks, and objects to get a result. For instance, the modes could include
Unlock
Repair
Damage
Password/ keypad Break
Power Source
Local Energy Disrupter (temp stop objects from working without damanging them)
Local Energy Field Distruptor (prevents things like teleporter and transmat beams from working)
Tardis remote call (brings tardis to your location)
The key would be to make it a puzzle game where you either have to avoid danager, avoid being shot, hide in shadows, solve puzzles, fix equipment and disrupt equipment, rescue Rose (I don't like the other on was much
) and setup traps.
But the most essential thing would be to have a baddy at the end of it, who ends up killing himself. The doctor always manuvers his enemies into a position where if they carry out their horrible plan, it all backfires on them.