First of all: You cannot "prosecute her" at all. Criminal charging decisions are made by law enforcement personnel and the District Attorney. Victims of crimes can report them and offer to participate in the prosecution, but they cannot compel the state to prosecute (or to decline to prosecute) anyone. Aside from calling the police to report a crime and following through with testifying about it, there is no such thing as "pressing charges" for crime victims.
Second of all, the facts as you state them do not conclusively give rise to proof of perjury. The officer can testify only to events for which he has personal knowledge. Presumably the officer was not present when you allegedly hit this woman; so he can't conclusively testify that you didn't. He can testify that she told him that you didn't, to impeach her; but that's not quite the same thing. It's important to recognize that memory is a slippery, elusive, and, at times, convenient thing. People don't remember everything completely, and their reports aren't always completely consistent and coherent. In any case, people are generally prosecuted for perjury only when they materially (that is, substantially) contradict themselves and they're under oath for both statements.
And sometimes, not even then. I've had opposing parties admit, under oath, to having lied under oath before. You can call the DA and ask that they be prosecuted, but if the DA's not interested, that's just how it goes. Of course, in any future litigation with them, you have a huge advantage - you can always ask them "So, have you ever lied under oath before?" and introduce the transcript of the court proceeding as proof. That is the remedy for inconsistent testimony under oath, more likely than any criminal prosecution.