Confusion: Caloric Intake vs Activity Output

I'm a 24 yr old female, 5'7", currently 124 lbs (BMI 19.4), have lost over 60 lbs in the last two years (did it verrry slowly, only adopted daily exercise into my life in the last year or so) and am onto my last 3-5 lbs.  I exercise 6-7 days/week (usually 60-75 mins cardio, 15-20 mins of strength training) and consume roughly 1300-1350 calories/day.  My family believes I'm not eating enough but I've read in various health-related websites that as long as you don't let your intake fall below 1200 (that "Daily Recommended Intake") then you're OK.  But I'm confused: if I'm putting in a total of 1300-1350 calories in my body every day (healthy foods: lean proteins, veggies, fruit, whole wheat carbs, etc) and burning off 600-800 during work-outs, do I need to compensate for the burn by tacking on an extra 600-800 calories each day?  I keep a food journal and I'm not sure how to log my daily intake: do I tally up calories to INCLUDE what I've burned off (i.e. total intake: 1800 calories, burned off 800, leaving a total of 1000 calories) or EXCLUDE it (i.e. total intake 1350 calories, burned off 800, leaving a total of 550 calories for the day)?  I gotta admit, 1350 calories plus intense work outs do tend to leave me pretty tired during the day but, hey, the weight is definitely coming off so I must be doing it the correct way, right?  thank you for the help!