Should a person have a goal to become a peer? "Why not?", I say! However, there is a difference between having a goal -- or perhaps an aspiration, and making the goal the only reason you do whatever it is you do. I have heard this called "the difference between having a 'right' goal and a 'wrong' goal". This particular discussion is close to my heart, because I've dealt with folk from opposite ends of the spectrum, and have myself been at opposite ends of the spectrum ...
There was a time before I was Laureled (I was living in Alaska/Oertha at the time), when I kept wondering why I hadn't been laureled yet. I started to get frustrated, and I concentrated on doing things to get recognition, and ... I found I wasn't enjoying the SCA - instead I was obsessed with being recognized. This all changed when I went to my first event in the central part of the West Kingdom, and met people who were active Laurels, and saw the work, and talked to people, and started to realize something about what a Peer really was. This was a major revelation for me, because at the time Oertha had very few peers (and no Laurels at the time -- the first Oerthan Laurel was asked to join the order six months before I was). It was hard to know what the expectations were, because Oertha was (and still is) very far from the center of things (however, now there is better contact, in general, with the central part of the Kingdom, then there was at the time ...).
Once I realized that my goal had become an obsession, and I realized I was going about things the wrong way, I relaxed. I backed off. I started to enjoy both the jewelry I was making (which is what I was eventually Laureled for) and enjoyed the SCA again.
On the other side of the coin, before I was asked to join the Order of the Pelican, I was doing what I was doing because it's what needed to be done. Yes, I sometimes wondered what I wasn't doing to be recognized as a Pelican, but I wasn't obsessed with it. I just continued doing those things because they needed to be done, and I (usually) enjoyed doing them. The day I was asked to join the Order, however, I collapsed at the King's feet because I was so surprised.
So, is it ok to have "I want to be a Laurel" (or a Pelican) as a goal? Why not? It's certainly considered ok to state "I want to be a Knight". However, don't let it become an obsession ... learn your craft, enjoy fighting (for the right reasons -- on the field of honor, fight for the honor of the person who's favor you carry on the field), and/or have fun being an officer (for those interested in service). Don't wear yourself out to the point that your only reason for going to events is to become a peer someday. Burning out is the wrong way to do it.
Do what you want to do, because you want to do it. Be a noble person. Don't worry about whether or not the "peerage is watching you" ... it is a lot easier on the psyche (not to mention the psyche of your friends, your significant other, your family ...).