My first thoughts are that the relationship sounds quite unpleasant and almost competitive, with little compassion or understanding shown to each other, but instead this almost legalistic approach ("precedents" etc).
Seconelyz for the purposes of this post I am going to assume that both of you find the need to walk the dog early before work an unpleasant shore? I am actually with you on this, I love our dog but I also love my sleep and morning routine. Whereas dog walks on the weekend are totally different - fun, relaxed, no rush, you can take as long as you like - it's one of the main pleasures in having a dog, and i assume if you didn't enjoy leisurely walks with it, you wouldn't have the dog.
I assume that when your partner agreed to the current arrangement, she did not work out of the homez so it made perfect sense for both of you that she walk the dog most week days, while you get to enjoy the pleasure and privilege of a relaxing weekend dog walk. Nice of her - she sounds like a supportive, understanding partner who was happy to prioritise your needs and happiness.
Not you both work and need to leave at similar times in the morning, it would be grossly unfair for you to insist on still only doing the fun, relaxed dog walks, whereas four days out of five your partner has to get up early (while you lounge in bed?) to perform the unpleasant chore of a rushed early morning dog walk before work. What gives you the right to pull this kind of rank on her? The fact that a different arrangement was made when both your circumstances were entirely different? That is so not cool OP, and if she accepts it, she is a mug. But why do YOY want to do this to her? Do you always prioritise your own happiness and needs, and entirely disregard hers?
I am amazed that anybody has said you are in the right. Almost to the extent that I wonder if I have misread the situation somehow? (Please accept my apologies and correct me if my understanding is wrong). Or maybe other people aren't understanding you? As you are vague in your posts about times, but it seems to me you will both now need to leave the house around 8:20/8:30. But you don't care about that and stoop think she should get up much earlier almost every morning, which you should enjoy the weekend walks?
The only possible fair solution is that you split monday-Thursday between you, alternate Friday, and enjoy Saturday and Sunday walks together, as a chance to strengthen your relationship and learn more about what makes the other happy......