Get some leather sew a seam and have a go on that first. I have done a lot, the main thing you should be worrying about is the thick seam part.I have not sown over a seam and I would try first. leather comes in different thickness, when I make bags and waist coat I did the thick sewing on my industrial walking foot machine.
Hugs Pam.

Please Please put a link up for this design as i would love to put it on a doggy coat for my own tiny dog who loves to go for bike rides in a bag at the front of my bike.

use a special needle that is made for sewing leather in the machine and use denim cotton thread for sewing the seams . Go slow and use a longer stitch than normal as a small stitch will cut the leather. A walking foot would also help with the sewing of the leathe.
Any problem with the leather not going under the foot smoothly can be over come by cutting lengths of normal kitchen roll into strips and placing a strip between the dog teeth and the leather . this will also work well if useing plastic or vynel

Haven't tried it yet but have accumulated some thinner leathers. I keep reading that you must use a light stitch design, otherwise you create a tear strip in the leather.

You can often find leather purses etc very cheap at thrift/OpShops etc so you could get one from there and cut it up first to have a play with it until you're confident, before you try the real project :)