Can You Take Tiny Dogs On The Plane With You And Does It Cost Extra?

You need to get an airline-approved carrier. For delta, this is a carrier that is:

Be constructed out of rigid plastic, wood, metal, or material of comparable strength with solid roofs. No cardboard kennels.
Have wheels that can be removed or made inoperable [applies to wheeled kennels only]
Have functional handles on the kennel's exterior to prevent tilting and any direct contact with the animals.
Close securely, but not lock, allowing personnel to open it in case of emergency.
Have labels with the words "Live Animal" in letters at least 1-inch tall on the crate's top and on at least one side.
Have upright arrow labels indicating kennel's correct Delta Air Logistics can provide these labels.
Contain some type of bedding, either shredded paper or towels, to absorb any "accidents."
Contain two dishes (one for food and one for water) attached to the inside of the kennel door. They must be easily accessible to Delta agents without opening the kennel door.
Display feeding instructions and food, if applicable. These instructions should be affixed to the top of the kennel, along with shipper and consignee information.
Not be made entirely of welded mesh, wire mesh, wicker, cardboard or collapsible materials.

and it needs to be able to fit in the seat in front of you. If your dog is not able to fit in that space, you will not be able to have it in the cabin, only in cargo.

To take the dog with you, you need to have a vet clear it's health in the 10 days prior to travel. This certificate must contain:
The shipper's name and address.
Any tag numbers or tattoos assigned to the animal.
The age of the animal being shipped (USDA regulations require animals be at least 8 weeks old and fully weaned before traveling).
A statement that the animal is in good health.
A list of administered inoculations, when applicable.
The signature of the veterinarian.
The date of the certificate.

You almost always will have to notify the carrier of your intent to carry a pet onboard prior to boarding. Your pet will likely count as 1 of 2 allowed carry-on pieces.

To determine the fee, call 800-221-1212 for flights within the United States


EDIT: For delta, you need to call reservations at

800-221-1212 or
404-765-5000

for them to tell you the correct size of the cage you will need. It varies by the plane you are on. Also you need to reserve space for your pet, so calling those numbers will allow you to do that.