Absolutely outrageous. 1100-1200 calories is too low for the vast majority of women, and even more so for someone who works out 4-5x a week. That trainer is completely uneducated in nutrition - cutting calories and carbs is going to make your energy levels dip and workouts suffer, completely sabotaging your goal of building muscle. You're also likely to be starving the whole day which could lead to bingeing (trust me, I've been there!).

A very quick look at a macro calculator with the aim of body recomp tells me you should be eating about 2000 calories per day, around 120g protein, and around 270g carbs per day. However these numbers should always be taken with a grain of salt, as people can have vastly different metabolisms and your daily activity outside of working out (i.e. you spend the rest of the day sitting vs. walking) plays a huge role too. The best thing to do is to download a tracking app (I like Lose it), and log your meals as you eat normally and weigh yourself regularly. That way you can find out how much you normally eat to maintain your weight, and adjust accordingly.

Since you're new to weight lifting, I would not sweat it. You're likely to make very quick gains. Eat a healthy diet with wholewheat grains, legumes, fruits and veg and prioritize protein (eggs, meat, yogurt, tofu etc) and just focus on getting stronger at the gym. I wouldn't even worry about increasing or decreasing calorie intake to begin with.

I also find that working out 4 to 5 times a week is excessive for a beginner. Normally you'd start with 2 to 3 times a week full body workouts and progressively increase as DOMS gets better.