I'm sorry to hear this, it's very sad to lose a beloved pet. I think the key with the kids is to use straight forward but age appropriate language and answer any questions they have honestly and clearly. Kids are very resilient and I've always found losses like this to be harder in fact on the adults than the kids (not to say it's not sad for them too of course).
At the moment I'd be letting them know that the dog is very old and sick and needs to go to the vets as a form of preparation, and then after it actually happens, explain in simple language like the PP suggested, tempting as it is to use euphemisms like 'passed away', 'put to sleep' etc with young kids it's much better to just say 'he died', 'he isn't coming back', 'we won't see him again' as less scope for misunderstandings and fear than if you try and dress it up with an adults idea of what is comforting (e.g. my well meaning aunt told me grandmother would always watch over me after she died when I was a bit younger than your kids, I was absolutely terrified at the idea of some kind of invisible corpse granny hiding in my bedroom/at school watching me, until eventually a kindly teacher asked what I was so afraid of and explained my aunt hadn't meant it literally 😂).
The death of a pet can often be a trigger for difficult questions from kids about mortality and death like 'what does dying mean', 'does dying hurt', 'are you going to die', 'am I going to die' and I think again you can answer as simply and gently as you can that death is a natural thing that happens when people or animals get very old and their bodies are worn out, that it means we don't see them any more and they can't come back. That sadly animals don't live as long as people and (Ddog) was nearly 100 years old in people years and that is very, very old indeed. That yes (whoever they're asking about) will die eventually but not for a very very long time, until they are very old like Ddog was too. If you do have a belief in heaven you can talk about that with them, but I wouldn't invent such a belief just to comfort them. If you like you can say 'some people believe that after we die we go to heaven, some people say don't know what happens after people die, just that they aren't there any more and can't ever come back (or whatever else), what do you think?'. Personally I quite liked the Lion King explanation of ''the circle of life' as slightly less nihilistic child friendly explanation of a non-heaven based after-life although it did prompt some quite challenging questions from my DC about the exact biochemical processes that make our bodies into grass!
The thing is as a parent you tie yourself in knots about this stuff but whatever you say so long as you say it with love, you listen to what they want to say, you offer cuddles and comfort and you acknowledge their feelings etc, you can't actually get it that wrong. I'd focus on talking about your lovely and happy memories of the dog and emphasize that him not being with us any more doesn't mean we lose those memories or can't think about him and talk about him. Encourage them to draw pictures of him or write down their memories, maybe think about what you can do as a 'funeral' for him even if you aren't physically having his body back with you, these rituals do really help kids and adults process their grief 