I am a lawyer and you are correct. Of course it would be the Department of Justice who makes the call on immunity. Mephistopheles has a better chance at getting frostbite than the DOJ granting this woman immunity so that she can be forced to testify before a Republican House Committee.
I thought Congress had the authority, via vote by each House, to grant immunity as well.
Also, she can provide a “proffer” (sp?) indicating what she would say if granted immunity.