Yes cutting down on carbs is a good thing, but don't make the mistake of cutting them out entirely. Don't think of cutting down, think more about controlling portions. Today's average portions are actually twice what they're supposed to be. For example, a pasta portion should only be a handful! It doesn't sound like much but pasta (or carbs in general) are only 30% of a meal! A meal should be 40% protein, 30% carbs and 30% Fat. Try avoiding red meats (they have a much higher fat content), instead go for white meats and fish (wholemeal toast, tuna in brine [not sunflower oil] and cottage cheese is an amazingly filling lunch and cheap too, I eat it ALL the time). Cereal for breakfast is also not that healthy (all carbs and very little protein), a full English breakfast is actually better for you (grill it and trim bacon to keep fat content down). High protein will help you build the right kind of weight (muscle), but you do need to use it or it'll be stored for later. Building muscle means that you'll burn more calories by sitting and doing nothing, always a bonus.
Exercise wise, ideally do 20-30 mins of heavy CV (Running, high impact sport, Zumba's quite fun!) 5 days a week. Or 1hour 30mins of light CV (walking, household chores) For the heavy CV, you need to be sweating like nothing on earth and have the urge to curl up and conk out when finished. If you have one of those baby rucksack things (my parents used to carry me in one) if it's a modern one, go for power walks (lots of hills) with baby in it. The extra weight will increase the level of the activity, and you'll be building muscle. Also, from experience, it's awesome being carried around in one!
Also increase water intake, I drink on average 4-5 litres a day. Yes you may spend slightly more time going to the loo (!) but it improves digestion, stops that morning after ache, and improves skin hydration! Win win!
Hope this helps and that it hasn't been too condescending! Best of luck!