Not really as soon as most people think. By "The 'I' In Team" (just about two months after Oz left,) it was quite obvious that Willow and Tara were more than just friends, and if they weren't lovers before "New Moon Rising" (six weeks or so later,) they certainly were after. So, from casual acquaintances to lovers in about three months or less.
On the other hand, Willow and Kennedy's first date in "The Killer In Me" is about nine months after Tara's death (in the Real World, that's not at all an unusual time frame,) and they also don't consummate their relationship until about three months later. For all her faults, Willow certainly can't be accused of jumping into bed at first glance. Well, some people do basically accuse her of that, but they need to get out of the basement more and meet some real people... 😉