Ajax Requests     

Quasar recommends Axios during project initialization: Use Axios for Ajax calls? (Y/n)

Then you should create a new plugin axios.js that looks like this:
(Here you can also specify additional settings for your axios instance)

import axios from 'axios'

export default ({app, router, Vue}) => {
Vue.prototype.$axios = axios
// ^ ^ ^ this will allow you to use this.$axios
// so you won't necessarily have to import axios in each vue file
}

Usage in your single file components methods will be like:

methods: {
loadData () {
this.$axios.get('/api/backend')
.then((response) => {
this.data = response.data
})
.catch(() => {
this.$q.notify({
color: 'negative',
position: 'top',
message: 'Loading failed',
icon: 'report_problem'
})
})
},

Usage in Vuex Actions for globally adding headers to axios (such as during authentication):

import axios from 'axios'

export function register ({commit}, form) {
return axios.post('api/auth/register', form)
.then(response => {
commit('login', {token: response.data.token, user: response.data.user})
setAxiosHeaders(response.data.token)
})
}

function setAxiosHeaders (token) {
axios.defaults.headers.common['Authorization'] = 'Bearer ' + token
}

Also look at Axios docs for more information.