Refer to an associated issue for JPA for what support should look like
The methods that should be supported in queries would initially be
LocalDateTime : getDayOfMonth, getMonth, getYear, getHour, getMinute, getSecond
LocalTime : getHour, getMinute, getSecond
LocalDate : getDayOfMonth, getMonth, getYear
These would need to be part of JDOQL string-based, as well as the JDOQLTypedQuery (hence have equivalent Expression classes).
Note that all of these are already implemented in DataNucleus, and there are JDOQLTypedQuery expression classes available.
Timing of this simply depends on the JRE that the next release of JDO is targetted at, since this needs Java 8.