My wife is a nurse and works at a hospital in a bad area, how can I convince her that she needs to get a license to carry ?

A reluctant gun owner is not going to effectively use a gun for protection.

Get her canisters of PEPPER SPRAY and with the money you would use for a licensed weapon, send her to take self defense classes.

Unless SHE is 100% ready, willling and able. a gun will be of no good to her.

Only fools carry guns.  Many Americans carry guns.  Many Americans get killed by guns.  People in other countries DON'T get killed by guns.  Americans believe that guns will make them safe.  Talk to parents at Columbine or Sandy Hook.  Once you carry a gun you up the ante.  People die.

You can get therapy to deal with you irrational issues.  Carrying a gun would put her in much more danger.  It would not be allowed in the hospital.  There is absolutely nothing positive that would come of this.  Gun owners, like you, are slaves to their fear.  You need to address the underlying issue, which is an irrational paranoia.  Get help, and then you'll be able to let go of your guns with your fear.

In my area, most hospitals are posted as "no gun zones" which would make it illegal for her to carry at work. If your wife works in a hospital similar, she couldn't legally carry there even with a permit. I would have her carry a large hat pin and know how to stab someone with it, or perhaps a can of mace.

Im all for the 2nd amendment and such but: 

A: If someone doesn't want to carry don't force them, its all about personal freedom and choice.

and

B: Nothing good can come for you with your wife packing especially when she divorces you and becomes your ex wife.

Why dont you pack and walk her to the subway?

Maybe you can buy her some bear spray.  That will stop someone in their tracks.  

Let her get a new job in a safer area.

 Unless you are very good with a deadly weapon, and willing to use it, it's not smart to carry one. You could encounter someone who can quickly disarm you and have your weapon for themselves. Guns kill more lives than they save! 

Women, and especially women who are in medical and caring fields are not typically very interested in carrying firearms.  Pepper spray, a tazer, a bat, these all work well and are less likely to trigger the woman's dislike of aggression.  I speak from experience here.  My wife is a midwife, and she often is alone and sometimes alone with women who have significant others who are violent and angry at the mothers giving birth.  She carries bear mace, a first rate tazer, and a spring baton.  

"...she’s from Australia where guns pretty much don’t exist. "

'Australians now own more guns in total than they did before the 1996 crackdown, according to figures from 2016.'

All that said, gun use and ownership is something she has to choose for herself. If she feels at all uncomfortable, that moment's hesitation is when the weapon can be taken and used against her.