She says that she had not known him a month. That would mean that it took less than a month for her to have no intrest in him, would it not?

I do agree, however, that had his behavior been more cordial, she might not have believe Wickham so absolutly. Though, if she had spoken well about Darcy ("He is a very polite,gentlemanly young man..."), I doubt that he would have said anything about his "ill-treatment" at Darcy's hands. Notice that Wickham goes fishing for information about her feelings on Darcy before he says anything.