No, it's not normal to lose that much weight on this diet.
You'll lose some weight by virtue of cutting out all the crap carbohydrates like bread, pastas, cookies, etc. But you sound like you're getting too thin.
Eat more food overall, but also try concentrating on lots of full-fat yogurt, ice cream, and those yummy baked goods Chelsea mentioned. Honestly, whenever I overdo it on just yogurt alone I put on a pound or two. If I was eating baked goods on top of that I'd put on 5 pounds in a week.
Don't forget nuts and fruit as well.
Good luck.
