Friend offered to bake our wedding desserts, but doesn't have insurance. Options?

No they would have to become licensed as a small business following all local regulations and procedures for baking out out of her home which is a health code violation in many areas. Her insurance would have to be business related as a professional vendor. She could provide desserts for a shower in someone's home, but unfortunately not at your reception. If you were having a backyard wedding in your own home, that would be different.

The type of insurance generally required by venues is public liability insurance, and any other applicable insurances and licences specific to the vendor type.

The exact requirements vary dependent on location and applicable laws so it is something you'd need to investigate but I suspect it might be quite costly for your friend to obtain.

Unfortunately wedding insurance will only cover you having booked everything, it will not cover the liability of your vendors to third parties.

At minimum, she'd need personal liability insurance, which is relatively inexpensive. Personal trainers, fitness instructors, people who teach photography or art classes, etc will generally get this. However for serving food or beverage the requirements tend to be stricter and require a commercial kitchen license or similar insurance, just because of the sanitation requirements, risk of food borne illness and disease transmission, etc. so I'm not sure personal liability insurance would be enough. She would need to follow certain standards and her home kitchen would need to meet minimum requirements (I had a friend who did holiday treat boxes and rented a small apartment that had a bathroom directly off the kitchen and there was no way she could get that kitchen certified). You'd be best to check about the requirements in your state.