So, I've been on a diet and exercise plan for going on 11-days today. I lost a lot in the first week (went from 167.5 to 159.2), but this week, I've been stuck at 159.2.

Does it sometimes help to increase the amount of calories you're intaking? I'm currently getting around 1,050 - 1,200 per day.

Or should I exercise more? It's frustrating to see such a big drop at the beginning and then nothing. :/

This is very normal in the second week of a diet. The first week you lose a lot of water as well as fat and see a big scale drop. Then it slows. But it actually takes a deficit of 3500 calories to lose a pound. That's 500 a day every day for a week.
In other words, fat loss takes time. If you're not too hungry I'd just carry on doing exactly as you are and be patient. If you're starving you could try increasing a bit. But relax....you're in this for the long haul.
Congrats on a great start!

I agree, don't worry too much, but maybe upping the calories will be helpful since you are also exercising and it would actually be better to have some slower loss to be healthier. You aren't terribly overweight, either, which is nice for you but may been that large losses are not realistic. Kudos for you to include exercise so you tone and get fit too.

I would recommend raising your calories to at least 1200 per day - anything less than that and you are putting your body into a dangerous place nutrition-wise.

I recently experienced the same thing... just this week actually... my weight had stayed exactly the same for a week and I hadnt changed a thing... before then, I had been loosing about 1/2 a pound to two a day consistantly. So this Tuesday I changed it up a bit, I drank a/b 20 more ounces of water than the usual 80, I did some cardio for about 30 minutes, instead of the usual leisurly walk, and I ate more frequently (not more calories, just spread out the food throughout the day.) Guess what?! The next day I had lost 2 pounds, did the same thing on Wednesday and today I had lost another 1.4 pounds.

Good luck and don't give up!!

I'm not sure if losing that much weight that fast could be HEALTHY but... it does certainly seem to work to shake things up a bit to shock your system, so you might want to try one higher calorie day a week or something as well (2000 calories maybe?)