2011 engine light shake when starting after new plugs

How many miles on her? Are you losing any coolant?
Where did you get the plugs?

 

Doesn’t mean a thing, but I’m not saying they’re counterfeit

 

There is a 99% change if you get it from ebay or amazon, it is the cheap chinese copies!

 

I buy my genuine Toyota parts through my local dealership's web portal, on a will-call to avoid shipping n handling charges. They will meet any "valid" advertised price for exact items posted. That means OEM part numbers and packaging clearly visible and must specifically state Genuine Toyota OEM part.
This assures me an actual genuine OEM part. I'm not sure if your aware of this, but Amazon n Ebay has distribution centers. Similarly boxed and bar coded items are mixed together, so even if you have an honest vendor - you may still get a counterfeit part. If something is shipped from the vendors' "own" warehouse; they have more control over what you get. But that means longer and pricier shipping time and cost.

 

Electronic parts are NOT the same as machined mechanical parts. You can see and feel the differences in a machined part; not so much on an electronic part. The mode of failure would determine what an electronic part would do or not do.
FWIW; I don't believe you have a spark plug issue, because the issues would happen at anytime your engine is running. ie. intermittent misfire and lower mpg. If your engine is rotating at 2K RPM; that plug is firing 2K times a minute - if there's a defect, you'll know it. IMHO. If you still have your old plugs; put them back in to eliminate that as the cause of your issue.

This is a good example.

 

Sadly, you can't trust any parts store any longer. They are about making money, so they buy the
cheapest they can. You have to be very careful. Look on the box and see where they are made.

I've gotten good Bosch plugs from autozone. I also look at the each spark plug box and make sure they
aren't made in china, rockauto totally sucks. Plain junk, NO customer support.

After market electronic parts don't seem to work well with the Prius.
Parts like the coils, and sensors, "if" you have to purchase them, it is very likely it will only be a 1 time thing.
So it's worth the extra money to get OEM parts.

 

could be the head gasket, ever cleaned the egr circuit?