We propose an insulating 2D phase of IrO$_{2}$, predicted by $textit{ab initio}$ evolutionary algorithms. The predicted phase is a van der Waals crystal, in which Ir forms a triangular lattice, and is energetically competitive with the metastable spinel phase, observed experimentally. Electronic structure calculations show that the magnetic properties of this phase are highly nontrivial, with an almost perfect degeneracy of 120$^{circ}$ $textit{Neel}$ and $Y$-stripe orders, and unusually soft magnetic moments. The resulting behavior, which we term $textit{easy plane anisotropy}$, is entirely different from what is realized in previously-explored Kitaev honeycomb lattices. Our results thus suggest that IrO$_{2}$ may be an ideal candidate to realize highly unusual magnetic properties.