Is Dettol Laundry Cleanser also a fabric softener?

No - Dettol Laundry Cleanser is an additive that kills 99.9% of bacteria, even below 30°C so that you can be confident your laundry is hygienically clean every time, whatever temperature you wash at (Proven to work in rinse cycle temperatures as low as 15°C). Just add it to your normal washing routine after adding your detergent.