It may be normal to dim a slight little bit. I would put a volt meter across the battery a fully charged batter should be 12.6 volts. Turn on the ignition switch to the on but not run position do you see an icon on the instrument panel representing a battery, if you do not see this battery icon the alternator is not seeing power to allow it to charge. Start the engine does the battery icon go out. A more complex but good diagnostic test is checking "voltage drop" on the battery ground and power cables. You can find a video on how to do a voltage drop test on youtube. Put a volt meter across the battery terminals with the engine off, at rest the battery voltage should be 12.6 volts if the battery is fully charged. Now get a friend to start the car while you watch the voltmeter, the voltage reading across the battery should read approximately 14.6 volts if the alternator is charging correctly. If the alternator is not charging correctly or sufficiently it will cause headlamps to dim when other electrical loads are turned on.
Thanks for the suggestions autotechpat!! I checked things out as you suggested. Everything seemed to be just fine. Now that I've been paying more attention to this, it seems that the headlights still dim when you turn on the cabin fan, but the brightness comes right back after a second or two. When the dimness was staying longer maybe the battery was just low for whatever reason or cold. I did note that the max voltage when my car is running seemed to be 14.3 volts, but I'm using a fairly cheap DMM and maybe I just needed to watch the voltage longer for it to peak at 14.6 V.