Flashing Fuel Pip with Full Tank. How long can I drive it? (Gen 2)

Yesterday, 12 miles after a complete fuel fill up, my 2006 fuel gage dropped to one flashing pip.
How long can I drive like this before it shuts down? Or will it shut down?

I suspect that the fuel level sensor either failed or broke connection. And a broken sensor is an expensive fix ($900+).

I would like to drive it to the dealer, and maybe drive even more, but I've read that the car will shut down, even if it is full of gas, requiring a tow and even more expensive repairs if driven to shut-down.

Does anyone know how this works?
How far I can drive?

Thank you!

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PS
-There is gas in the tank -- it is almost full (no leaks or theft).
-I tried the fuel gage recalibration sequence, but got only dashes during the odo sequence.
-I have not checked the electrical connection to the gas tank/fuel sensor (I would like to but have not found that. Where is it?).
-My dealer said it will shut down, but didn't know how long I have to drive it.
-I can typically drive 80+ miles on a flashing pip, but I am not sure if this issue (a faulty fuel level reading?) will behave the same way as a normal flashing pip.
-I have not checked error codes (should I buy a tool and do that?)

 

That last fill up was around 10 gallons.

 

Thanks WJTracy. I don't want to hurt the batteries.

So has anyone out there run with a broken fuel gage? Stuck on 1 flashing pip?

I was under the impression that the system would shut itself down after x miles past the low fuel warning. Maybe that does not happen?

 

Update: Spoke with 2 different toyota service techs. they both said it should be fine driving indefinitely with a broken gas gage (blinking 1-pip) as long as I don't really run out of gas. I drove it to the dealer, 5 miles out, the gas gage jumped back up to full. So the problem went away.

At the dealer I got the oil changed. They also checked and "recalibrated" the fuel gage for $60 which seems reasonable.

Not sure what happened. And hope it doesn't happen again.
Thanks!

 

Andrew and Paul,
Thanks. This is good to know since I don't think anything has been fixed, so the issue may come back.

Paul, yes, the mileage on the consumption screen did reset upon fill-up. So I suppose something was working properly then. We drove it another 20 miles or so today and it's still fine.

Got really close to buying a 2016 Eco Prius today, but decided to hold off