You can petition for her now or wait until you are a citizen. I suggest you speak with an immigration attorney for more information. My firm is experienced in spousal based immigration petitions.Ask a similar question
You can sponsor her now, but the waiting time is currently 4 years. You can also wait until you become a U.S. citizen, but if you recently received your green card, this could even be a longer wait.
You may want to consider whether she would be eligible to enter the U.S. on a temporary visa.Ask a similar question
It sounds like you may be interested in sponsoring her for a fiancee visa. You should consult with an immigration attorney who can identify several paths that you can take to make things go quicker and/or reduce the amount of time that you are apart from your girlfriend. Then you can chose which path is right for you.