As a sole proprietor you probably don't need an EIN (depending on your state) but it won't hurt you to get one. It's up to you.
This is a bigger decision than just this show. If you call it a partnership you are saying that she is your PARTNER in your business, which will include her business. That gives each of you the benefits and liabilities of being partners. If you have no partnership agreement defined, it probably will mean you two are 50/50.
I would recommend you each file separately, if only because it will be easier on your taxes. Otherwise, you can consider her an employee for the show or an independent contractor, but that will still cause tax issues. Check out your seceratary of state's website. That will usually have all the information you need for small business requirements