Airlines usually do not allow passengers flying with dogs to sit in bulkhead rows, business or first-class cabins with lie-flat beds, or emergency exit rows. Also keep in mind that airlines will not accept pets on the plane if temperatures are forecasted to be too hot or too cold at any destination along the route.
Can dogs sit in first class United?
Two pets per flight are allowed in United First, United Polaris Business and United Business (select aircraft only). No pets are permitted in United First, United Polaris Business and United Business on Boeing B757 200, B767, B777 or B787 aircraft (due to inadequate storage space under the seat).