As long as you are over 21, and are legally allowed to possess a firearm, you may carry a firearm INSIDE your vehicle in any manner.
You can carry it loaded or unloaded. On the seat in plain view, or in the glove box. You can even carry it on your person. As long as you do not remove it from the vehicle on public property.
I highly reccommend getting a CCW. Then you may carry it outside your vehicle as long as it is concealed.
I always reccommend checking Missouri statutes for yourself and not taking anyone's (including mine) advice on the law. Remember, it will be you going to jail if you break it. Just do a search for RsMO 570.10 for CCW law. I'm not sure what the vehicle carry statute is, but I also reccommend printing it out and carrying it in your vehicle in case you run into a Law Enforcement Officer who isn't knowlegeable about the legality of vehicle carry.