A skorn is too good if you don't have much money at the start, but if you have much more fun with dw, then try to change your weapons as soon as possible, but this all depends on your aims.
Do you want play on low monster power (0,1,2) for maximum experience and items or do you want to play on higher monster power (7,8,9) for more challenge and longer fights.
If you want play on low monster power for experience, your gear is good enough to farm efficient, but you should buy another helm with a socket for a ruby. I would suggest an IK Helm. Furthermore you should try to get a Hellfire ring.
Just use the skorn untill you can afford decent weapons.
skorn is only good for paper dps or if you don´t have any gold.
dualwield is always better than skorn for a ww barb since high attackspeed makes it alot more effective.