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State management is the keyword, which might help for your further research.
Especially vuex, as the most popular Vue state management library probably makes sense in your case (https://www.npmjs.com/package/vuex). There are tons of tutorials out there.
If you don’t want to use a state management library, you can implement a simple version of it on your own by saving the data in the localstorage or in the cookies. Or – if it’s just about the age, you also could add it to the query params.
There is also a pretty well described SO answer for a similar question: Vue: shared data between different pages
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This is not the best way to do it.
You could implement /edit/:name/:age. But what happens if you access the URL /edit/Carl/999?
You should fetch the data, such as name and age, by a unique user id instead: edit/:userid.