Hi! Bit of a wannabe nutritionist here (starting a course next year!). At your current weight and height, yes, it is a bit unhealthy for you to go so low, and your body will have difficulties shedding weight long-term.
I hope you don't mind, but I put some of your details into a website that calculates how many calories you need to have per day to lose 2lbs a week and it came out with around 1700kcals at your height and current weight. This is regardless of exercise - you can eat the *burnt* calories back and go over 1700 on a day where you do that extra bit of exercise. However you may want to lose more than 2lbs a week, in which case you may not want to eat those calories back
As you're pretty active, you'll probably notice a good loss on 1700.
I'm a big fan of eating as many calories as recommended to lose weight, because then if you start to plateau you can recalculate (with your new weight) and reduce as needed - if you start on 1200 and then plateau, then you can't really reduce by much more without damaging your health too much, at your height.
As you've been functioning on 1000kcals a day, you may be thinking "oh god how can I increase to 1700 without gaining weight!". You may well gain weight in the first week or two at 1700 whilst your body readjusts from not starving itself, but after a few weeks you'll be losing again. An easy way to increase the number of calories you eat without being unhealthy or feeling like you're stuffing yourself is simply by adding things to your meals. E.g. adding some nuts to your cereal, cooking with olive oil, adding avocados and olives to your salads, drinking more milk / fruit juice. Good luck!