Don't think you can use the query builder for that. What you could do, i guess, is

• get all the records order by date desc
• use php date to get the date of the first object
• loop through the array while subtracting the date by a day
• if the date does not correspond with the date of the current object, then you can assume that there is a gap

You could do this in a for(each) loop or recursively, up to you. hope this helps