I can't comment on rates because I live in an entirely different continent to you, but this idea that use of the client's home and wifi is a notable perk is in my opinion not valid. You are the one providing the service of caring for the dog in its familiar environment, which necessitates you being in their home.
Yes, it's nice that you can use the wifi. But that is not a big deal.
Aside from your care of the dog, the time you will spend walking and feeding the dog, there is also the opportunity cost to you of what you could be doing INSTEAD.
Sometimes you are fortunate: the dog has no anxieties about being left alone and the owner gives you permission to leave the dog alone for several hours. This is clearly a more challenging case and not being able to leave the house for a 9 hour stretch is a severe burden on you. For me, that would warrant an increase in my normal charges.
My advice is for you to look what other sitters are charging. If you can find no examples of other sitters, look what boarding kennels are charging. Use of the client's home and wifi is not a consideration. Do this a few times and you will find a price point at which you are comfortable.
You will from time to time come across extremely strange owners who are very concerned with whether you use their wifi, TV, how much water you use, what temperature you set the heating to. Some of them will have nanny cams and will obsessively watch you. If you get bad feelings about an owner, do not accept the booking. Owners are (presumably) humans, and some humans will always try to take advantage of or even outright scam others.