12V 1.5A is equal to 18W, and even if USB can supply that much power in the first place (going by the comments to the question, there seems to be a bit of uncertainty about that) it's going to strain the USB ports quite a bit. USB 3.0 can provide up to 900 mA at approximately 5 V on a single port, which works out to 4.5W of power. In principle it should be possible to use a DC-DC converter to bring this up to 12V, but what you gain in voltage you lose in current. If you could draw the full 900 mA from four USB 3.0 ports, then you would just hit that 18W target, but DC-DC conversion isn't lossless, so in practice you'd need closer to 5-6 USB 3.0 ports all capable of delivering full power when the computer is running on battery to guarantee that you'd keep the drive running. I don't think your laptop has those specs.
Instead, if you are worried about sudden power losses, there are two options which I think deserve serious consideration.
If you were in the position of buying a new drive, you could pick a 1.8" or 2.5" one, since they are generally able to be powered solely from USB, not needing an external power supply. This option is of little use to you since you already have the drive, but may be of interest to others in the future.
That leaves a second source of power, independent from the mains as well as the computer's USB bus. Hence, the suggestion in the comments to get a dedicated UPS to power the external drive through. Even the smallest dedicated UPS should be able to power something drawing a few tens of watts with a yawn, so you could simply pick one based on what's cheapest and probably get something that will power the external drive just fine basically for however long you wish, easily allowing a controlled shutdown.