Another vote for trustedhousesitters.com. My husband and I are members and have used it to get house/pet sitters for several trips, even trips over a month. We also use it as house/pet sitters ourselves. It's great. We've scored free stays in London, Wales, Scotland, and many places in the US. We love animals and adore pet sitting as a way to extend our travel funds. We have made lifelong friends by pet sitting, both as home/pet owners and as pet sitters. Long before there were websites, I was pet sitting for friends here and there as well. It's a great thing to stay in a home rather than a hotel room, and to have pets to love, cuddle and care for. As a pet/home owner, I had peace of mind knowing there were people I trusted who were paying lots of attention to my cats and occupying the home while I was gone.
If you decide to put up a profile, here's some advice. Since you have at least one elderly pet, I would describe the duties of the pet sitter in a clear, loving way. Don't sugarcoat it but don't make it more complicated than it is. This may dissuade some people, but you didn't want them anyway. Your profile should highlight the attractions of your area and your home. House sitters are looking for fun places to travel to. There are also digital nomads who house sit as a lifestyle and aren't as focused on the exact destination. Make sure to arrange phone calls or video calls with people whose applications you like. Have them arrive a day before you leave so they can participate in doggie care before you leave. It's also nice to cook a meal to share with your pet sitters. Communicate about your expectations and desires about communication while you're gone. When I pet sit, I send pictures of happy pets at least once a day for the first week. Pet owners love their pets (as you know!), and they tend to appreciate the pictures and short texts letting them know all is well.
Do have a plan B ready in case something happens. A website like trustedhousesitters.com doesn't have an automatic backup if your sitter falls through or has to leave due to an emergency. A service like Rover can be a decent fallback, though it will cost you money.
Feel free to PM me if you want to chat more. Also, if you decide to sign up, please contact me or one of the other posters who referred you -- we can all get free months using a referral link.