New Twiddle

components.my-component\.js

import Component from '@glimmer/component';
import { inject as service } from '@ember/service';

export default class extends Component {
  @service router;
  
  get qp() {
    return this.router.currentRoute.queryParams.qp || 1; 
  }

  incrementQp = () => {
    this.router.transitionTo({ 
    	queryParams: {
        qp: Number(this.qp) + 1 
      }
    })
  }
  
  incrementModel = () => {
    this.router.transitionTo('with-model', this.args.model + 1);
  }
}

router\.js

import EmberRouter from '@ember/routing/router';
import config from './config/environment';

const Router = EmberRouter.extend({
  location: 'none',
  rootURL: config.rootURL
});

Router.map(function() {
  this.route('with-model', { path: '/:model' });
});

export default Router;

routes.index\.js

import Route from '@ember/routing/route';

export default Route.extend({
  redirect() {
    this.transitionTo('with-model', 1) 
  }
});

routes.with-model\.js

import Route from '@ember/routing/route';

let count = 1;

export default class extends Route {
  queryParams = {
    qp: true
  }
  
  model(params) {
    return Number(params.model) + count++;
  }
}

templates.application\.hbs

<div>
  {{outlet}}
</div>

templates.components.my-component\.hbs

<button {{on "click" this.incrementQp}}>
  Increment QP
</button>

<button {{on "click" this.incrementModel}}>
  Increment Model
</button>

<div>
  Model: {{@model}}
</div>

<div>
  QP: {{this.qp}}
</div>

templates.with-model\.hbs

<MyComponent @model={{@model}}/>

twiddle\.json

{
  "version": "0.17.1",
  "EmberENV": {
    "FEATURES": {},
    "_TEMPLATE_ONLY_GLIMMER_COMPONENTS": false,
    "_APPLICATION_TEMPLATE_WRAPPER": true,
    "_JQUERY_INTEGRATION": true
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/3.5.1/jquery.js",
    "ember": "3.18.1",
    "ember-template-compiler": "3.18.1",
    "ember-testing": "3.18.1"
  },
  "addons": {
    "@glimmer/component": "1.0.0"
  }
}