12V Battery: Age, voltage and warranty

I have a new to me 2012 Two Prius which I bought just a few weeks ago. Today, I checked the 12V battery for both manufacturing date and voltage.



It looks like the battery was manufactured on October 10, 2013 and was installed in July 2014. This means the battery was replaced within first two years of the vehicle's life. This information is nowhere on the Toyota service records, which is strange because the battery is Toyota.

Second, I checked the voltage under the hood. I used the positive terminal in the fuse box and the negative probe was connected first to the engine metal and then to a bolt behind the fuse box. In either location, I could not get a stable voltage. It kept jumping between 7V and 0V. I was using needle probes so may be the contact wasn't good. This battery runs without any problems, but given its age, I am going to replace it. This brings me to my final question.

If I bought a new Toyota battery from an online dealership and installed it myself, could I access the warranty at any dealership across the country? My local dealer wants over $250 including taxes whereas I can get it online for $165 shipped.