Hello there, lovely! To age up your dog in Sims 4, first you need to get a 'Sim's best friend' satisfaction reward or purchase the 'Age-Up Treat' from the vets.
Oh, how do I get the 'Sim's best friend' reward?
Sure thing! For that, you need to have a high enough friendship level with your pet. Once it's high enough, you should receive the reward. You can also take the pet lover aspiration that makes it easier.
And for the 'Age-Up Treat', where can I find it?
You can buy the 'Age-Up Treat' from the vet clinic, darling. After you've bought it, go to your Sim's inventory, click on the treat, select 'Give to...' and choose the pet you want to age up. Just like magic, the pet will age up!