You cannot do a between query using just the month and day on a date field. A date field stores values as ‘YYYYMMDD’. There is no way that I know of to query between to values that only include the month and day. You might be able to query these by using a REGEX value query, but this would not work to get values between two months.
The only way to do this would be to have a field that only contains just the month and day.
