Will I gain weight once I increase my calories?

I've been eating 1400-1500 cal per day for the past 8 months and my weight dropped almost 30 pounds. I'm a little underweight now at 5'9 and 122 but, although I'm quite thin, I don't look too thin because I have a small, narrow frame. The thing is, my menstrual cycle stopped with my last period being in March. Also, my weight is still dropping. I weighed 126 just a couple of weeks ago. I know this isn't healthy and my doctor recommended I put on a couple of pounds and increase my calorie intake and, although I'm near petrified of gaining weight, I'm going to make myself do the right thing to be healthy so I am going to start eating more. I'm planning on starting to increase my intake to 1600 for a couple of weeks, then 1700, and then 1850 or so since that's what I'm told is the approximate amount I should have to maintain since I'm not sedentary. My body is used to having a lower amount of calories in general (although for the past few months I've allowed myself a couple of days in the week where I eat 1600-2000) so should I expect weight gain? If so, how much? Can I prevent my body from gaining more than a couple of pounds?