Do I need to disable remote key fob if parked for two weeks?

nope, just park it like any car, make sure you don't leave any lights on. if it was 4 years or older, or you were leaving it for more than a month, it would be wise to purchase a jump pack, and learn how to use it. if you ever have to have it jumped, it's a good idea to watch the jump monkey to make sure he doesn't cross the positive and negative.

 

it disables itself after two or three days/

BION
StarCaller

 

On 2nd gen Prius there's a button under the dash to disable some fob-searching mechanism. There's no button on 3rd gen, and apparently the system is reworked so there's no need to do anything.

Ten to fourteen days is kinda iffy, you may or may not have issues when you return. Likely not, but a borderline battery might have troubles. There's always a slight drain on the battery when installed; if it sits long enough there will be problems.

A good practice for airport parkers is to stow a fully charged, good quality jump pack in the car. Some are flat enough to fit in the hatch sub-floor tray. Clore JNC660 is my preference.

 

The 12V battery should lose only about 10% of its charge capacity per week to vampire drains and self-discharge while the car is parked, so it should easily survive a two-week wait, IF it starts out healthy and fully charged.

 

all the best.