I am 5'6 and weighed 9st 9ibs (size 12) three months ago. Am now 8st 12 (size 10) and I did it through a 1200 diet on weekdays and 1500 on weekends plus upping my exercise. I've now upped my calorie intake to 1800 most days (with about one day a week where I tend to go out for a meal or have a takeaway or whatever and probably eat a lot more) and seem to be more-or-less maintaining my weight and dress size.
I started off just by eating lots of salads and fruit and veg and didn't find I was losing anything. Not sure why but I then started weighing and writing down every single thing I ate to make sure I was sticking to about 1200 calories - it turned out that left to my own devices I seemed to be having the odd biscuit or whatever and not really registering it and I didn't realise how many calories were in the odd treat. I was also some days eating nowhere near 1200 calories as I was eating so much fruit/veg. If you eat too few calories your body goes into 'starvation mode' and your metabolism will slow as your body tries to hold onto your weight, 1200 calories is usually recognised as the minimum you should eat. So now I record everything I eat so that I know if I've gone over/under the 1200 and can vary it the next day accordingly.
I also agree you should try to eat as much protein as possible as this will make you feel fuller. I'm vegan and my typical day's diet when I was on 1200 calories looked like this:
Breakfast: Soya protein shake
Lunch: Soup with roughly 200 cals and 10+ grams of protein (bean, lentil, pea soups are best veggie ones)
Dinner: One of the following: A big salad with tofu and mixed seeds, veggie sausages with lots of veg, lentil dahl with pitta bread, vegetable stir fry with tofu, ratatouille with soya chunks, couscous with TVP bolognaise
Snacks (had a few each day to take me up to 1200): Fruit, soya yoghurt, energy bars (eg: food doctor, nakd, eat natural), popcorn, ryvita/oatcakes with peanut butter, handful nuts and dried fruit, ice lolly, chocolate rice cakes, toasted pitta bread or crumpet, carrot/cucumber sticks with hoummous. I would have the occasional treat (eg: chocolate, biscuit, cake) as well but not often.
I tried to make sure I was having something with plenty of protein for dinner and a moderate amount of protein at other meals too. I took a vitamin supplement with added iron and B-vitamins. Aim to eat 1g of protein for every kg of body weight you weigh, so at 60kg you should be aiming for 60g of protein a day. As you're veggie and can't eat soya that may be more difficult for you but look in health food shops for alternative meat and soya-free sources of protein as they do exist. You can buy whey or pea-based protein powders to add to shakes which are a good idea. Also make sure you're eating plenty of dairy products, eggs, nuts/seeds (they are high in fat but as the rest of your diet is probably going to be fairly low-fat I wouldn't worry about it - some fat is good and necessary) and lots of beans and legumes (peas, lentils etc). I added nutritional yeast flakes to some of my soups or meals as this contains a high level of protein (plus added B vitamin inc. B12) and I liked the cheesy(ish) taste.
That said I was not trying to conceive on this diet so I do agree with the above posters that you should check with your GP before going on a low-calorie diet whilst you are undergoing IVF.