Welcome to our wonderful forum! My first question would be "have you previously owned a cat?" If so, you throw everything out the window because a bengal is not your typical cat. While they are gorgeous and wild looking, they come with challenges. Many times owners are not prepared and can't deal with them.
An F4 bengal means it is 4 generations removed from the Asian Leopard Cat (small wild cat in Asia) which started the bengal breed when bred with an Egyptian Mau or a domestic shorthaired kitty. While the F1's (the litter from an ALC and a regular kitty) through the F3's are considered "early generation" bengals, your F4's are considered domestic cats and are allowed in almost all the states in the US and almost all countries.
Bengals and dogs can get along, however, when getting a bengal kitten know they will have boundless energy (which will continue the rest of their lives). Your doggie is older and may not want to be the playmate to a territorial bengal. Your bengal will be very vocal! Not just communicating, but will howl up a storm for no apparent reason! Your bengal needs a lot of wand toys and play sessions, a tall cat tree, a couple of litter boxes, and should not be allowed to roam outdoors unless on a harness and leash. They can be trained to walk just like a dog.
There is plenty to read on this forum. "Behavior" is a great topic as you will encounter some of the situations bengal owners have incurred and you may gather information from the responses. I would never discourage someone from getting a bengal, but I do encourage you to find out ALL you can about the breed and be prepared for a LOT of patience. They can be the best pet in the world and they can be challenging at the same time. You need to go in this with an open mind and be prepared to spend time blending your family. We here LOVE our bengals and wouldn't trade them for the world (most of the time).