Is 1000 calories per day safe?

Not correct. 1200 is the minimum. So you can run a 379 calorie per day deficit by eating 1200 and safely lose 3/4 lb per week. Sorry. Small people get the short end of the stick with this stuff, but you should focus on safety first and not try to exceed 3/4 lb per week. In the long run you will be happier, healthier - and thinner - if you stick to safe dieting and not try to push it further than that.

MFP will not let you set a goal below 1200 in the Goals tool. Give that tool a try and see what it comes up with.

Also-you’re already well within a healthy weight for your height. How much are you planning to lose?
Have you considered doing a recomp (eat at or near maintenance but do a solid, progressive lifting program to adjust your body composition-less fat, more “toned” - but minimal or no actual weight loss).

I’m 5’4”, on my way from 133 to 125 (127 now). No, that amount of calories is not healthy or sustainable. I had set myself at 1300 (plus exercise calories), but am losing a bit too quickly for comfort, so bumping up to 1450. I walk and lift weights 5-7x/week, but no high impact stuff. The walking gives me about an extra 200 calories a day, so I feel pretty satisfied with my amount of food (important for consistency) and I can get my nutrition in with occasional treats (important for health and consistency).

Strength training will help a lot in reshaping your body—which will make the bigger difference in how clothes fit. Though at our size, a pound or two seems like a big difference in clothes!