how long would it take me?

I'm 5ft 2", weighting 142llbs at the moment.
Was wondering how long it would take me to lose 20lbs eating 1300 calories a day and burning 600 calories through exercise a day?
Ive never been this heavy, usually weigh around 130lbs. Lightest being 120lbs.

It all depends. Everyone is different. I'm 5'1" and it took me two years to get from over 170lbs to 109lbs, I'm almost 52 and apparently have a slower metabolism because I had to eat low to get that, and still have to eat lower compared to younger girls the same height. Plus different people have different metabolism.

Too many changes at once can be hard on some people. I've always eaten healthy so it easy for me to simply eat less. Eating at a calorie deficit is hard on people; even a small deficit puts your body in a state of flux with hormones and such. Everyone is different. Some people can handle a deeper calorie deficit than others, this is not right or wrong, it just is. Stress in your life affects your hunger hormones; lack of sleep, fatigue, job stress, family stress, financial stress, etc. Add in emotional eating issues and it gets even more complicated. Most people can only handle so much change/stress at once, they try to do too much and fail. Sometimes it might be a better strategy to eat at maintenance and make some small changes first, it really depends on how much stress you are taking in at the moment.

Your body loses weight in chunks, not linear. I have found that you can do everything right and your weight loss seems to plateau but if you are patient and keep exercising and eating at a deficit (however slight) you will lose it, it will suddenly "whoosh". There are so many variables for the scale; water retention, digestion, hormones, allergies, sodium, carbs, water intake, DOMS, inflammation, the list goes on. People mistakenly think they lose or gain weight when they eat more or less because of these fluctuations.

Losing weight requires tremendous patience. You will not lose it when you want it or where you want it. The body does its thing. Some apparent plateaus can last a month or so. You cannot make it happen faster. You must focus on two things; calories and exercise. Nothing else matters. Scales and metrics don't matter. The day in and day out grind of exercise and calories are all that matters. It is not very exciting until things fall into place. You get your victories and you ride one victory to the next.

The scale is a trend tool. The scale is good but put it away and only check once a week and only use it as a trend tool. It will fluctuate, it does not matter. Take front side and back progress pictures at least once a month. You will see differences that the metrics won't tell you and it's that little bit of NSV that will keep you going until the next victory.

It depends on what you are eating and how you are exercising; also, if you are taking medications and how much stress you are under. Everyone is different. You could lose it in a month, or it could take you a year. Calculate your BMR and set your net at that number. 1300 may be too few calories for you which could slow your metabolism.