How to attach quarter-round molding to the base of a shower stall
Is that wood quarter round? I would encourage you not to use that and find PVC quarter round if you insist.
For install I would first silicone the end of the laminate gap where it butts into the pan and let it dry. Then attach the quarter round with a bead polyurethane construction adhesive to the pan only on the vertical surface, or better yet schluter kerdi-fix if you can find it. Then silicone the edges and hope there is enough allowance for movement. Ideally there would not caulk the gap with the laminate but I would be more worried about water intrusion than expansion and contraction.