Hi Nairhita,
Yes, you have understood it correctly that if the axis is reoriented, the particle moves in a new direction. However, I'm not sure if you have got the point of the quaternion. This quantity specifies the orientation of the particle, and hence its direction of self-propulsion, which remains constant, provided there are no torques and thermal fluctuations. However, it does not 'provide an axis and angle in which particle will rotate' in the sense that it is not an angular velocity; but perhaps we are just miscommunicating.