My usual disclaimer: I'm not an expert at anything.
It's my understanding that most hard drives set aside some spare sectors that can be used in place of damaged sectors. I don't know how many are set aside. I've read some articles that say 10% of the HDD is set aside. On a 500GB drive that would be 50GB worth of sectors. If one sector is 512 bytes then two sectors would be 1 kilobyte. That adds up to a lot of spare sectors at 10%. Even if 1% is set aside, that would be 5GB worth of sectors on a 500GB drive. But unless I'm really off on my math, your 1300 bad sectors should be more than 4KB if each sector is 512 bytes. This article gives some more info about hard drives in general and how sectors work. NTFS.com HARD DRIVES. Hard Disk Drive Basics.
Should you get a new hard drive? I'd think strongly about getting a new one. But even a brand new drive could have bad sectors due to manufacturing glitches. Or maybe a bad drive slipped through quality control. Just copying data from the old drive to a new drive would not copy bad sectors. They are physically a part of the drive. Bad (corrupted) data could get copied.