Yes. You can safely ejaculate inside her as long as she remembers to take her pill every day at relatively the same time. Wait until she has finished her first pack of pills, however. Its good to let her body take some time to get used to the pill before you begin relying on it. When she starts her next pack, you should be good to go! You will be over 99.9% protected against pregnancy as long as she remembers to take her pills!
Also, remember that vomiting/diarrhea can make the pill less effective as the body may not have sufficient time to absorb the hormones if this occurs. Also, there are certain medicines that contradict the pill and may make it ineffective. Complete lists of these medications are online, but the most common one is antibiotics. If your girlfriend has to go on antibiotics, then you should use a back up method (like a condom) for at least a week after she has stopped taking them.
If you're careful, you'll be safe!