I am that way if I run at night...I actually don't have enough energy to run the whole run. I LOVE running in the morning. I love hearing the birds greet the day, I love having no traffic, I love that the sun hasn't made it 1000 degrees yet. I have noticed ever since I started running in the morning, I can't sleep in anymore though. Today, I have a run at night, so I can't run this morning. So, I was planning on sleeping in and resting, and my body woke me up anyway.
Also, just pointing out, if you are a morning person, the energy will eventually come. Your body needs a bit of time to adjust to the extra exercise...but then it gets happy about it.