Thank you for your favourable comments, Artlady! Actually, no, it is not reversible. That kind of double-knit uses 2 colours simultaneously, whereas this was tubular double-knit which is knitting in the round on 2 straight needles. So, the colours look the same on the outside and on the inside.
My daughter hasn't worn the hat yet, but I am hoping that she will, or I may be asking her to give it back lol.