Hey,
Firstly, congrats on the birth of your baby. I just had a baby girl four and a half months ago and absolutely adore her, and i understand about trying to find time to exercise, it is so hard.
Anyway, in regards to your calorie intake, it depends on whether you are BF or not. Most people should not eat less than 1200 calories a day or your BMR (basal metabolic rate) will drop, and your body will go into starvation mode, and then muscle will be lost and not fat. Your calorie intake should not be less than about 1500 if you are BF. They are absolute minimums. After all, it is better to increase exercise than lmit cals too much! Keep in mind also, that 1gm of fat is equal to 7 cals whereas carb and protein are equal to only 4 cals.
As for exercise, i brought myself an exercise bike so i can ride on it and watch movies at the same time. I also take my daughter walking everyday to help. I also have the 'Aussie Fit' program (i don't know if it sells overseas) and that was only $10 a video where most are around $30. Cheap and effective. It's a bodysculpt program that has a video on each part of the body for 30mins and a couple of cardio workouts for 45mins each. They are great!
I have the same weightloss goal as you (120lbs i am currently 140lbs) and i think a sensible diet of 3 meals a day, and an hour of exercise is a simple and effective way of losing weight or at least getting fit.
Good luck