You can absolutely upgrade the SSD in your MacBook Pro. Your particular model uses a 2.5" hard drive / SSD, which is different from the Retina MaBook Pros and newer MacBook Airs which use a more proprietary design.
This SSD from iFixit would be compatible with your MacBook Pro: [gekoppeld product ontbreekt of is uitgeschakeld: IF107-115-1]
There are options as well for upgrading past 256GB as well, for example: http://eshop.macsales.com/shop/SSD/OWC/M...
I use Other World Computing (OWC) as the example in the link above but most manufacturers are making SSDs that would work with your MacBook Pro. You might shop around a bit keeping in mind that you it needs to meet the following requirements:
- SATA connection
- 2.5" form factor
- 9.5mm tall (or thinner/shorter)
Installation for your machine would be extremely similar or identical to these steps:
Mid 2012 MacBook Pro Hard Drive Installation
For what it's worth, in case anyone comes across this while searching, you CAN upgrade the SSDs in MacBook Airs and MacBook Pro Retinas as well, it's just a different design that isn't as popular yet. I think what gets confused when thinking of upgrades in the MacBook Pro Retinas and the MacBook Airs is that the memory (RAM) is soldered into the logic board, essentially making it impossible to upgrade. The SSD though is an mSATA form factor with a slightly different connector, which makes it kinda proprietary but does still allow for replacement and upgrades if a replacement part is available. OWC is one of the first companies to sell these but I'm sure there are others as well, could be worth shopping around. The installation is even relatively straight forward, requiring only the bottom case to be removed and the battery to be disconnected, at which point the SSD is removed by unscrewing one screw and removing from it's socket.
OWC MacBook Pro Retina SSD upgrades
OWC 2012 MacBook Air SSD upgrades
They have SSD upgrades for the other two generations of new MacBook Air as well, easily found on their site.
Hope that helps!