C.!
you can totally do this!
my first advice is to not push it. don't set a deadline, eg: must be 40lbs lighter in 3 months. fast is just as unhealthy as carrying the extra weight.
aim for a pound a week. it's the healthiest way and the easiest way for it to stay off.
with PCOS your insulin is off as well, so your cells eat up the sugars and store fat moreso than if you didn't have PCOS. with this challenge you might want to shoot for 30lbs instead of the full 40, or maybe even 20. you also should discuss this with your doc, as s/he might have some drug options for you that would help - maybe you're on metformin already, but if not it's worth a dicussion.
i lost 40lbs - a little more than 1lb a week- this way:
a) multivitamin. a one-a-day burns 500 extra calories a week.
b) 30-45 minutes of cardio a day. at first i did every other day, and then i loved it so much i bumped it up to 6 days a week. in my experience it's best to plan your 45 minutes FIRST each day. not first thing, but of all the things you have to do, make the time for the workout and then plan everything else around it. it's the one thing you are doing for YOU. and you deserve that time 100%
c) do a workout you like! if running on the treadmill sucks, dont' do it! a brisk walk outside in the neighbourhood is just as good, if you like that better. an aerobics class at the gym (i like those b/c you have someone telling you what to do for an hour and boom you're done, plus there is daycare for Tommy)
d) being a vegetarian sounds like you have a decent diet, but even so, think about what you are eating. to maximize your efforts, eat smaller meals, more times a day. 5 meals, less than 4-500 calories a meal. bowl o' cereal here, tuna sandwich there, if you need a calorie list, there are dozens online. your gym might also have one! tells you how many calories are in what. i keep clif bars handy - they're vegan.
e) free weights. turns out building muscle acutally burns more calories longer than the cardio. just slower. grab a couple 5lb or 8lb weights and look online for an upper body workout, and then lunge lunge lunge. :) or again, the gym.
the only thing you need to do is be confident that you CAN do this.
best of luck to you!!
C.