Very generally speaking, your body needs carbohydrates (and fats and proteins) to function properly. Carbs give you energy. Even if you were not running at all, you would still need to be eating carbs regularly - ideally at every meal! So in a nutshell, yes, you definitely need to make sure you are consuming an ample amount of carbohydrates to fuel your half marathon race and during your half marathon training.
As far as "carb loading" is concerned, this may actually mean different things to different people, depending on what your typical carb intake is. For those runners who are conscious about getting in at least three meals and one or two snacks a day, and are focused on making sure they they have a well balanced plate of fats, carbs, and protein at every meal time, you might find that you only need to increase your carbs during half marathon training by a little bit in order to fuel yourself, since you are already taking in carbs regularly. The half marathon distance is certainly a long distance and needs proper nutrition and hydration, but if the body is being regularly fueled and not restricting any foods or food groups, then you will be stronger and more ready to run a half at your fastest pace. However, if you are regularly restricting your intake - especially your carb intake - then not only will your body be sluggish and tired, but your brain will not be able to function properly either.
You've got six months of planning before your race, so my advice if you are not already doing so, would be to take an honest look at what you are eating on a regular basis, and make sure you're getting enough carbs in - and if you're not, start adding them! Remember that carbs aren't just pastas and bread - fruit, honey, oats, and cereals are excellent sources of carbs. See how this shift in nutrition effects your running and how you feel, then continue adding in carbs if you recognize you have been depleted of them and it makes you stronger. (and yes - don't be afraid to eat a carb-heavy meal the evening or two before your race!)