I know there's a lot of talk about 'fasted cardio' on an empty stomach, and some people get results with it, but im not a big believer in it.
When you eat a good combo of protein and carbs before exercise, this gives you more energy to perform a better workout (you'll burn more calories if you can work harder and for longer).
The reason people do it is because first thing in the morning you have less sugar stored in your body, so fat is there to be burned. Or so people beleive...
In reality, your sugar (or carbohydrate) stores don't just evaporate overnight. Your muscles are still filled with glycogen (carbohydrate in its energy form) so you won't really be burning 'just fat' as many people assume.
Either way, trying to isolate and burn only fat isnt a very effective strategy for weight loss. Its actually sugar (carbs) stores that you want to burn. This is because people tend to eat a lot more sugar than fat, and any unused, excess sugar gets converted to fat.
As I've said before, sugar and salt are the enemy, fats aren't as bad as people make out, since we eat a whole lot more sugar than we need to (we even eat sugar thinking that its healthy, in the form of bread, rice, pasta and fruit juice etc)
Anyhow, with walking your not causing much of a metabolic effect so its really not worth thinking about effects of pre- or post-workout calories and that sort of thing.
Just get out there, start moving and watch your sugar intake.