Molecular deuteration is commonly seen in starless cores and is expected to occur on a timescale comparable to that of the core contraction. Thus, the deuteration serves as a chemical clock, allowing us to investigate dynamical theories of core formation. We aim to provide a 3D cloud description for the starless core L 1498 located in the nearby low-mass star-forming region Taurus and explore its possible core formation mechanism. We carried out nonlocal thermal equilibrium radiative transfer with multi-transition observations of the high-density tracer N_2_H+ to derive the density and temperature profiles of the L 1498 core. By combining these observations with the spectral observations of the deuterated species, ortho-H_2_D+, N_2_D+, and DCO+, we derived the abundance profiles for the observed species and performed chemical modeling of the deuteration profiles across L 1498 to constrain the contraction timescale. We present the first ortho-H_2_D+ (110-111) detection toward L 1498. We find a peak molecular hydrogen density of 1.6_-0.3_^+3.0^x10^5^cm^-3^, a temperature of 7.5_-0.5_^+0.7^K, and a N_2_H+ deuteration of 0.27_-0.15_^+0.12^ in the center. We derived a lower limit of the core age for L 1498 of 0.16Ma, which is compatible with the typical free-fall time, indicating that L 1498 likely formed rapidly.