Species tree estimation from genome-wide data has transformed evolutionary studies, particularly in the presence of gene tree discordance. Gene trees often differ from species trees due to factors like incomplete lineage sorting (ILS) and gene duplication and loss (GDL). Quartet-based species tree estimation methods have gained substantial popularity for their accuracy and statistical guarantee. %To address ILS, accurate species tree estimation methods, such as ASTRAL, TREE-QMC, and wQFM-TREE, have been developed. However, most of these methods (e.g., ASTRAL, wQFM, wQMC) rely on single-copy gene trees and models ILS and not GDL, limiting their applicability to large genomic datasets. ASTRAL-Pro, a recent advancement, has refined quartet similarity measures to incorporate both orthology and paralogy, improving species tree inference under GDL. Among other quartet-based methods, wQFM-DISCO converts multicopy gene family trees into single-copy gene trees using DISCO and applies the wQFM algorithm on the single-copy trees. However, ASTRAL-Pro has remained the only quartet-based summary method to explicitly model gene duplication and loss. In this study, we extend both wQFM (which requires quartet decomposition) and wQFM-TREE (which operates directly on gene trees) by modeling gene duplication and loss, leveraging the concept of speciation-driven quartets introduced in ASTRAL-Pro. Our algorithm consistently outperforms ASTRAL-Pro across most model conditions, offering a promising alternative for species tree estimation in the presence of GDL.