@Stephanie365 - on Airbnb you cannot be a "business" in a profile, you must always be a human which means you and your personal information as the host will always be attached to the listing. Having an umbrella policy to cover you and your belongings will cover you sufficiently should be anyone bring suit. You are still covered under Airbnb's umbrella with regards to lawsuits and then subsequently be covered under yours before typical property insurance kicks in. Having the LLC doesn't not protect you from someone bringing a lawsuit or going after your personal assets because the platform is set up as you as the host (the business does not "host").
Additionally, once the property is governed by a business entity, you are now bound to business rules set by the state in your home. This includes being held accountable for sanitation, business licenses, inspections, and since you have a farm, agriculture and other government agencies that may be required to check up and inspect livestock, etc. You will likely be required, as the working host, to get a sanitation certification. Being a casual at-home business as a regular human is much different than being a licensed business who rents a piece of property that is now beholden to the same standards as hotels. This is the biggest complaint of the big chains because casual renters are not held to the same level of control.
You absolutely must talk to a local attorney and business advocate to ensure that you know exactly your liability with regards to factors other than lawsuits. Most Airbnb hosts do not do this and do not realize the reach of their exposure. Just read about how quickly laws are changing in cities across the country.
Good luck.