Your question fails to take into account the rent that you'll presumably be paying during the 'saving' period. Unlike the mortgage payments that you would otherwise be paying, that's all 'lost money' (in that you'll have nothing to show for it in the long run).
I'd opt to start house-hunting now but (unless, say, a change of work location forces you to move home) not rushing into anything. If you do find your dream home within a month then go ahead and buy it - but don't worry if you're still looking for it many months later.