For a two-hour dog walk/sitting visit, would you double the amount for a one-hour visit?

You could, depending on how busy you are right now. If you have a lot of clients right now, and this person is OK with your double rate, go for it!

I personally charge less for any additional time on top of my regular rate, but I do take into consideration whether I am walking a small dog or a large energy dog who wants to spend 2 hrs running with me at the park.

But since you are asking for a walk/sitting visit advice, does this mean you are house sitting, charging a house sitting fee per 24 hrs? In that case I would not be doubling my rate, but that's just me, you are obviously free to charge whatever you feel is appropriate. As long as your client is ok with your rate, then I say you and your services are worth it, and your client appreciates you. After all, many people have only now realized how hard it is to take care of their dog! Many of them never used to understand that dog walking and boarding is a real and hard job, until now! (I remember when I started walking dogs in 2015, it was kind of new a thing in my area, and some people were shocked when I told them I charge $8 an hour! More than a few then even said something like :"OMG you want to get paid for dog walking? I thought you're doing it for free! It's just a dog walk, nothing difficult" ). Yep, a lot of people didn't understand what kind of a service they're getting, when you come to them, you take care of their pet, you can be trusted with a key/house etc... So I am confident to say, times have changed, as many people got a pet during this pandemic, and now they're returning them back to the shelters because they realized that pet care takers are really working hard!

Good luck with your business! :)

I'd suggest considering all factors when making that decision: How busy is your calendar? Is this a regular ongoing client that books frequently? How much work is this pet(s)? Ease of interactions with pet owner?

In some cases, you may find yourself comping the time (at no extra charge) and in other situations, you'll charge more for your time.