You don't need dry ice.

We took coolers for years to many destinations. I am a fan of poplar bear coolers but cheaper one work good enough.

The key is to freeze everything good and hard. I am talking freezing it for days, not buying something fresh the night before and freezing it for a couple of hours.

Make sure the cooler is packs tight and don't open it.

I have used cardboard to line the cooler and used techiice sheets but honestly, this was probably over kill. We have done 36 hours door to door with everything being solid on arrival.