That's some kind of cobra. In the 22 images this wiki has of basilisks, the only one with a hood is on the Danish book cover, so presumably they don't have hoods.
Link between Basilisk and Horcrux
Due to Herpo the Foul has been the first to create a Basilisk and a Horcrux, is it possible that when he created both, it was done to one to be opposed to other or it occurred naturally (due to some natural magical law)? By definition, one is opposed to other, since a Basilisk kills a living being and a Horcrux maintains a being's soul alive. Andre G. Dias (talk) 13:05, April 5, 2014 (Brazil)
About another discussion, is it possible that Voldemort discovered about Horcrux after searching the origin of basilisk (after he discovered the Salazar Slytherin's basilisk) since both were created by the same dark wizard, Herpo the Foul? Andre G. Dias (talk) 13:11, April 5, 2014 (Brazil)