I weigh everyday and intend to do it for the rest of my life. It was not weighing that got me to 346 lbs. However, I learned very quickly that the scale fluctuated every day, and I had to learn to deal with that. It is completely normal for it to fluctuate, depending on what you've eaten, what you've drank, if you've had a bowel movement, if you've exercised recently and your muscles are retaining water, etc. And you should always weigh the same time of day - preferably after awakening and peeing. I always weigh at least 6 lbs more in the evenings than I do in the morning.
If it continues to bother you to see it go up and down, you may want to consider only weighing once a week. But you may be like me, and once you realize that it's normal, you may want to weigh everyday anyway.
Either way, I don't think you need a new scale.
One last thing to think about - you mention that you are keeping your calories pretty low. You are close to my starting weight - and you're taller and much younger - so I know that you could still easily lose weight eating at/near 2000 calories. One thing about starting with your calories low is that it is extremely easy to get really hungry and binge and then get thrown off plan. If you are hungry, you might consider raising those calories. Save those really low calories for when you only need to lose the last 5 - 10 lbs. Otherwise set yourself up now to be successful by making it as easy as possible.