The law takes effect on July 1st. So that means on June 30, you would not be eligible to buy a second handgun within 30 days, unless you qualify for one of the currently existing exceptions. The next day, July 1st, you should be able to.
Of course with as much computer troubles as they have... it will be interesting for everyone (not just you) to see if it works. Anybody else expecting to be in a position to test the new law?
* g. A person who trades in a handgun at the same time he makes a handgun purchase and as a part of the same transaction, provided that no more than one transaction of this nature is completed per day;