JS form verification
Is this the easiest way of doing it?


In my view, yes: I don't see how to dramatically simplify your code.
It only can be (very) slightly reduced using return false; instead of e.preventDefault;.  

You also might use the more common $(document).ready() in place of $(window).load().
BTW it'd be more readable to rename your checkPets() function to something like mustPlayMusic(), which reflects that it returns a boolean.

So it results in:

$(document).ready(function(){
  $('.pets form').submit( function(e){
    if(mustPlayMusic()) {
      $('body').append('&lt;audio&gt;&lt;/audio&gt;');
      $('audio').attr({'src': 'audio.mp3', 'autoplay': 'autoplay'});
      return false;
    }
});


On the other hand, something puzzles me: the checkPets()||mustPlayMusic() function doesn't match the conditions you detailed above.  

It should be:

function checkPets () {
  var cat = $('#checkbox1').is(":checked");
  var dog1 = $('#checkbox2').is(":checked");
  var dog2 = $('#checkbox3').is(":checked");
  return (cat &amp;&amp; (dog1 || dog2)) || (dog1 &amp;&amp; dog2);
}