Router bit suitable for straight cuts in pine 1/2" deep; Dutchman door patch
If you don't want it to take a long time, why did you purchase a low-end router? You won't be routing anything 1/2" deep with that thing successfully, I'll predict. Indeed, it's generally not a smart idea to try routing that deep in one pass with any router, but you'll be limited to nibbling away in tiny increments with a small-shank underpowered tool. If it's additionally plagued with poor bearings it will work even less well. And you'll be stopping to charge batteries on a regular basis.

More directly to your question:
Since you are using the tool you have purchased, and it only takes 1/4" shanks, you'll be looking for a 1/4" upcut spiral bit. And you'll be "standing there for hours," except when you are sitting somewhere else waiting for batteries to charge. 

Or you'll buy a half-decent (or decent) plug-in router with a 1/2" shank and be done a lot faster.