On that diet you'll probably go into ketosis, simply because there are so few calories that your body will have to burn fat to obtain any energy. Unfortunately you will also go into starvation mode - slowed metabolism. Also since it's too low in protein (and every other nutrient) you eventually start digesting your own muscle tissue. Too far into starvation and important muscles like the heart get injured.
That's not a maintainable diet, and it's definitely not paleo. A low carb paleo diet would have you eating high fat, moderate protein and low carb. Ketosis and more importantly becoming adapted to burning fat will come with that and it's not going to have you starve. On low carb paleo (note that low carb and paleo are not synonymous) you'd skip the banana and have a pork chop or a burger. And a lot more food.
Use a meal tracker like cronometer.com and find out what you are really eating. 1200 calories per day would be bare minimum for a sedentary adult* female losing weight. If you are at all active, you'll need more than that. You also want to make sure your nutrient intake is adequate.
*teenagers need more because they are still growing.
Paleo can help those of us who are overweight lose weight, but it isn't a weight loss diet. It's a health acquiring diet.