The binary intermetallic compound TiAu is distinguished by an extremely sharp and narrow density of states peak at the Fermi level that has been proposed, via scattering between mirrored van Hove singularities, to be the mechanism for antiferromagnetic ordering versus the more fundamental ferromagnetic, Stoner instability. Here we study, using density functional theory methods, magnetic tendencies and effects of doping, the latter within the virtual crystal approximation (VCA). Ferromagnetic tendencies are quantified using the fixed spin moment approach, illustrating the strong Stoner instability that does not however provide the ground state. Use of VCA results allows the identification of the value of the Stoner exchange constant I = 0.74 eV for Ti. Magnetic fluctuations not included with semilocal density functionals are quantified with the procedure provided by Ortenzi and coauthors, with alloy concentrations corresponding to the quantum critical points reduced by a factor of three to five. Our results provide useful guidelines for experimental doping studies of TiAu.