This is a hard question, since it depends on what you mean by "spirit".

First the official doctrine (from D&C section 93): "Man was also in the beginning with God. Intelligence, or the light of truth, was not created or made, neither indeed can be." I think that says pretty clearly the doctrine that we all are co-eternal with God.

But wait, you might say, doesn't Mormon doctrine hold that God is literally our Father, the creator of our spirits?

Now for my own (possibly erroneous) stuff. Basically, the following is an attempt to reconcile the above scripture with the concept of God as the Father of our spirits. I think there is a difference between the term "intelligence" and the term "spirit". Basically, to me a "spirit" seems to be an intelligence which has been placed inside a spiritual body (which would probably look like a regular body, but of course not made out of flesh and bone). Our intelligences have always existed, but God created our spiritual bodies, in that He placed the intelligence (which presumably makes up the core of our identity) inside those bodies. This would include Jesus-- God the Father created Jesus's spiritual body. This could be an analogy of our physical birth, in which our spirit body was placed into a physical body.

Now when this creation of spiritual bodies happened on the eternal time scale is difficult to say. It could easily have been before the creation of this universe, or could have been "outside" time as we know it. My personal view is probably the latter-- I do not believe that God is bound by our view of time, but rather lies outside of our universe of 4-dimensional space-time.