Tuesday morning

I am beginning to seriously doubt the value of these early morning 10k runs.
For a start I have to get up at 6am which is really very early in anyone's book and then I'm running on empty for over an hour. I feel exhausted after a couple of miles and there are still 4 to go.
I do feel quite good once I've stopped though.
But for the rest of the day I feel weary.
I know it's good exercise - but would it be better to run after work when I've had something to eat during the day? Or is running on empty a good thing in terms of getting round to burning fat for energy which is what I'm aiming for? The low-carb thing obviously won't help even an evening run - slow-release carbs might but I don't know the rules about them. And should I really be bothered about rules? It's not like I'm following the plan strictly, just cutting out bread, pasta, spuds, rice and sugar. I think it's working - put it this way: I'm going to 2 parties this weekend and am wearing clothes I wouldn't have dreamed of wearing just a few weeks ago - so I guess I feel more confident if nothing else.
Keep on runninggggg......