As long as you're sure it's what you want to be doing that's fine - personally I don't see it as particularly healthy to be cutting out any food types from your diet - particularly when the one you're cutting out is your bodies best fuel for the activity you're taking part in! Though again, our goals are different
For improving speed, just google 'speedwork sessions' or something and you'll be sure to find plenty to suit - personally I'd be looking at 400m-1600m repeats, though some with 200m repeats may well be worthwhile too considering your goal distance.
Do you think you'll perhaps take part in any races? or is it purely to compliment your weight training to help burn fat?