Spread the ladyfingers on a tray. Mix the coconut milk and rum. Spread over the ladyfingers so that they soften slightly (use more coconut milk if necessary).
Mix the quark, rum, coconut milk, desiccated coconut and cane sugar. Whip the cream with the cream stiffener until stiff, fold into the quark mixture, spread on the soaked ladyfingers, smooth out.
Chill for approx. 24 hours. Drain the pineapple. Decorate the tiramisu with pineapple and coconut chips.