My DD was tested for Precocious Puberty at 7- I remember how worried I was - can't imagine how you must feel with DD at 4.
At the hospital - they examine them- their breast(if they're growing) and their pubic bone and ovaries- DD's consultant just felt these areas.
They also X-rayed her left hand- with precocious puberty the 'bone' age differs from their physical age.
Bloods were taken as well.
The consultant had my DD back for 6 monthly appointments, but when she reached 8 was happy to discharge her as 8 is classed as a 'normal' age to start puberty nowadays.
Also with regards to the PMT- DD suffered with this too, her consultant Okayed me to give her Evening Primrose Oil capsules- which helped not only the PMT , but her breasts were very tender too. Best to check with that though- with your DD being the age she is.
With regards to explaining- I explained in simple terms that when we reach a certain age our bodies change slightly so we can have babies, and that DD's body had started that change a little early.I also gently and simply explained about periods, as we still have no idea when they will start , but wanted to prepare her rather than they happen and she be terrified she's dying or something.
Obviously our experience is different to yours- my DD was just monitored as another poster said, probably your DD will be treated with Hormone injections.
Good Luck - I know how scary it is- and it's hard to understand yourself let alone for your DD.