Utilizing Vuex simplifies the solution to this issue

Live demonstration on netlify

View the code on github https://github.com/manojkmishra/animalfarm

GetAnimal.vue (Axios call disabled for testing; hardcoded data used)

 <template>
 <form v-on:submit.prevent="getAnimal()">
   <textarea v-model = "animal" name = "animal" type="animal" id = "animal"
   placeholder="Enter your animal here">
  </textarea>
  <button class = "custom-button dark-button"
  type="submit">Get animal</button>
  </form>
 </template>
 <script>
 import axios from 'axios';
 export default 
 {
    name: 'App',
    data: function() {  return { info: '', animal: ''  }  },
    methods:  {
        getAnimal: function()  {
            // axios
            //   .get('http://localhost:8088/animalsapi?animal=' + this.animal)
             //   .then(response => (this.info = response.data),
                this.info={"fur-color": "yellow","population": 51000,"isExtinct":     
                            false,"isDomesticated": true },
                this.$store.dispatch('storeAnimals', this.info)
                //);
        }
    }
 }
 </script>

DisplayAnimal.vue

<template>
<div>
<p>Animal name: {{stateAnimal.animal}}</p>
<p>Fur color: {{stateAnimal.furColor}}</p>
<p>Population: {{stateAnimal.population}}</p>
<p>Is extinct: {{stateAnimal.isExtinct}}</p>
<p>Is domesticated: {{stateAnimal.isDomesticated}}</p>
 </div>
</template>
<script>
 import {mapState, mapGetters} from 'vuex';
export default {
computed:{  ...mapState({ stateAnimal:state => state.modulename.stateAnimal }),   
 },
}
</script>

modulename.js ( store module)

export default
{
 state: {stateAnimal:null,  },
 getters:{ },
 mutations: 
 {    ['STORE_ANIMALS'] (state, payload) 
    {  state.stateAnimal = payload;  
    console.log('state=',state)
   },

  },
 actions: 
 {  storeAnimals: ({commit}, data) => 
    { console.log('storeanim-data-',data);
      commit(  'STORE_ANIMALS', data   );  
    },     
  }
  }

Index.js (for vuex store), you can disable persistedstate as its for saving state if page is refreshed

import Vue from 'vue'
import Vuex from 'vuex'
import modulename from './modules/modulename'
import createPersistedState from "vuex-persistedstate";

Vue.use(Vuex)
export default new Vuex.Store({
plugins: [createPersistedState({ storage: sessionStorage })],
state: {  },
mutations: {  },
actions: {  },
modules: { modulename }
})

State is available/shared for all the components

To start off, consider creating a new folder named "services" and within it, add a file called service.js for your axios calls - this is not only good practice but also contributes to cleaner code organization. Next, implement Vuex for managing this type of data effectively.

Regarding the structure, assuming GetAnimal.vue serves as the parent component while DisplayAnimal.vue is the child component where you want to display the information. To test if this setup works, utilize props. Additionally, you can pass data from the child back to the parent using $emit(). It's highly recommended to incorporate Vuex for state management in this scenario.

Creating a Vue component named 'product' which takes a prop named 'message'. The message prop must be of type string, required and has a default value of 'Hi.' It renders the message within a div tag.
  
  // In another component where an axios call is made, this is how you can include the 'product' component: <product message="hello"></product>

To ensure a seamless user experience, I would pass the animal name/id as a route parameter to the display page. This way, the component responsible for fetching and displaying the relevant animal data can prevent users from encountering an incomplete page if they visit the display page directly through the URL.

If you need to share local state between pages, consider using Vuex as suggested by others.

EDIT:

As requested, here is some code added to my answer.

Routes:

const routes = [
  { path: "/", component: SearchAnimals },
  { path: "/viewanimal/:name", component: DisplayAnimal, name: "displayAnimal" }
];

DisplayAnimal.vue:

<template>
  <div>
    <p>Animal name: {{animal.name}}</p>
    <p>Fur color: {{animal.furColor}}</p>
    <p>Population: {{animal.population}}</p>
    <p>Is extinct: {{animal.isExtinct}}</p>
    <p>Is domesticated: {{animal.isDomesticated}}</p>
  </div>
</template>

<script>
import axios from "axios";

export default {
  name: "DisplayAnimal",
  data: () => ({
    animal: {}
  }),
  methods: {
    fetchAnimal(name) {
      axios
        .get(`http://localhost:8088/animalsapi?animal=${name}`)
        .then(response => {
          this.animal = response.data;
        });
    }
  },
  created() {
    this.fetchAnimal(this.$route.params.name);
  }
};
</script>

SearchAnimals.vue:

<template>
  <form v-on:submit.prevent="onSubmit">
    <textarea
      v-model="animal"
      name="animal"
      type="animal"
      id="animal"
      placeholder="Enter your animal here"
    ></textarea>
    <button type="submit">Get animal</button>
  </form>
</template>

<script>
export default {
  name: "SearchAnimal",
  data: () => ({
    animal: ""
  }),
  methods: {
    onSubmit() {
      this.$router.push({
        name: "displayAnimal",
        params: { name: this.animal }
      });
    }
  }
};
</script>

This example is basic, lacking error handling, but it offers a starting point for implementation.