When I first went vegetarian, I had a really awful period in the second week, similar to "withdrawal" symptoms. It was apparently my body going into "shock" especially if you usually have a very routined week in terms of "meals" (for example: If you have say, fast food every Tuesday, your body MAY protest when it doesn't get all it's additives, even though it's bad for it!) It did pass though... However if you're fainting, don't ignore it.
Make spinach and lentils your homeboys. Even potatoes have iron in them! So do nectarines (100g has about 8% of an average adult's RDI), cashes, bok choy... The list goes on. Try snacking on nuts throughout the day. Some people are worried this will make you "fat" but you have to remember that being vegetarian, if you're not relying on processed soy like veggie nuggets or veggie hotdogs, etc, and cutting back on dairy (go you!) it's VERY low calorie. You should be getting at LEAST 1000 calories a day ( about 4000 kj, do NOT get the two confused, you'll feel AWFUL only getting 1000kj in a day!) - The recommended calorie intake for adults is anywhere from 1500 to 2000 calories.
Also, if possible, add a berocca effervescent to your morning glass of water. THE FIZZY ONES ONLY are suitable for vegans/vegetarians (the gel caps are coated in gelatine) and contain HEAPS of B12, vitamin C, calcium and a bunch of other stuff. To my knowledge and internet searches, unlike multivitamins, if you intake too much of a certain vitamin from it or your body is already getting enough, it just flushes itself out of your body when you pee (sorry for the TMI, but I couldn't think of a nicer way to put it!)
Most importantly, see and discuss it with your doctor. I was a bit dizzy and it turns out I was used to my "old" diet of 2 big meals a day (I know, so unhealthy!) now I eat about 5 times a day and drink lots of water (I'm also a bandit for green tea.) A simple blood test can show if you're low in iron, b12 and various other minerals. If you are, these can be easily supplemented if necessary.
Thanks for the tips

Yeah. I think my new diet shocked my system a lot. Not that I ever at a lot of meat/dairy. Maybe on 2-3 times a week max. My sister is vegetarian, so a lot of our meals were vegetarian anyway. But, the lack of dairy/meat would have plummeted my caloric intake. EEK! Which I'm silly, and didn't even think of. I've had a day full of food

Haven't felt dizzy or lethargic yet. I am also taking the iron tablets, and I did notice that I was looking super grey under my eyes last night (that's always been a sign that I'm anemic again... it happens easily for me) which is why I just went and got the iron tablets straight away. Made sure they didn't have any gelatin or anything in them either, cause some do. Just had a snack of wholegrain toast with almond butter and strawberries on top

Best thing ever. I will be putting spinach in my carrot/apple/ginger juice from now on as well. Just to make sure

Thanks for the suggestions too