This is a dog backpack made from a cheap commercial backpack from any noname brand you'll find. (as you can see, the basic tutorial is in french and that's my native language so please excuse me if I get it wrong)

Supplies

a pair of scissors
a seam ripper
strong nylon thread
4 meters of nylon strap
2 metal rings
3 strap adjusters the same width as your nylon strap
1 parachute buckle

Step 1: Unstitch the Slings and Handle of Your Backpack

Keep all the parts for the following steps

Step 2: Seperate the Pack in Two

Roughly cut between the outer pocket and the body, keeping a two to three centimeters margin after the zippers for stitching

Step 3: Extract Canvas

You'll find yourself with a lower part of the now cut bag made of two distinct entities : the inside of the bag cut in half, and the lower (front) pocket.

Unstitch the upper part maintaining said pocket (fig. 3), then retrieve the canvas separating the two parts (between the backside of the front pocket and the frontside of the main bag) for further use. Make sure you keep it intact.

The goal is to end up with the backside of both of the pockets composed with the padded rear of the original backpack.

Step 4: Setup the Top of Your Bag

Sew two perpendicular and one parallel bands of nylon strap on the retrieved canvas to reinforce it.

To make the handle, take a 20 to 25 centimeters nylon strap. Fold one extremity on 4-5 centimeters, pin it to the parallel strap of the canvas.

On the other extremity, fold it so that it catches the metal ring,on 6-8 centimeters, and pin it the same way.

Sew your future handle to the two perpendicular straps. Stitch in a "X inside a square" pattern, with three rows of stitches for a resilient attach. Fold about one meter of nylon strap into a bias tape and sew it along the canvas with the handle.

Step 5: Add a Collar and Chest Piece

Take two pieces of nylon strap of a generous length and sew them to both sides of the top of the bag, on the short edge, with the same box-and-cross shape than before

Put everything on your dog's back and determine the right length for your straps so that they fall in the middle of their chest

Put a strap adjuster on each strap

Fold and sew them there around the second metal ring

Take one of the slings, fold and sew the strap by one of its extremities to the metal ring

Take 15 centimeters of nylon strap and make a buckle. You'll set it up atop the sling so that it reaches the place where the ribs of your dog end. Cut the excess off and make a clean seam at approximately 1-2 centimeters from the buckle.

Step 6: Finish the Saddlebags

Turn the two pockets inside out, stitch solidly the open tops, up to both ends of the zippers, and turn them back around.

Unstitch them right in their middle to insert nylon straps inside. On one side, insert just enough length to put the enclosure of the parachute buckle. On the other one, make sure you have enough length to place a strap adjuster, the other end of the parachute buckle, and still fits your dog.

The right setup is when, with the harness in place on your dog, you can still put one hand between the dog's chest and the straps. Make sure to properly balance the weight between both sides, and that the total weight of the bag + contents doesn't exceed around 30% of the dog's weight to not injure his or her joints! Keep it cool, let them get used to it.

Sew everything together with a box-and-cross stitch pattern like before.

Step 7: Sew All in Place

Through their open zippers, stitch the two pockets' backsides to the top of your bag.

Make a 2 to 3 centimeters wide rectangle, along the full length of the long edges of your top canvas. Make 3 to 5 passes, then stitch criss-cross to make multiple crosses.