I do think is too early if all you're deploying are two services. Kubernetes is a great tool for orchestrating containers at scale. While it solves some of the problems you'd have (rolling upgrades, maintain containers available) I don't think that the complexities of operating a cluster might be worth at the sage you're at.
If you're in AWS, I'd recommend looking at fargate to get you started. It'll give you some of the benefits you mention, but without the overhead of managing the servers. Once you reach a higher scale, or once you have lots of services, then I do recommend you look at Kubernetes. Another thing worth looking at is Heroku.
One word of advice: If you decide to use Fargate or Heroku, try the hardest to keep the environment specific stuff outside of your containers (e.g. don't call any Fargate or Heroku specific APIs in your container). That will make your eventual migration to Kubernetes a lot easier.
PS This advice assumes that you are looking for a way to quickly manage your app. If you're looking to learn more about kubernetes, then, by all means, go ahead and use it for this! I'm a big fan of it, and I do think that Kubernetes is on its way to becoming THE cloud standard (disclosure: I have a company that builds products to help develop with Kubernetes).