Etiquette question: is there such a thing as accepting an offer 'too early'?
Actually, it is simple courtesy to accept as soon as you know you will do so. This helps the institution deal with its obligations to you and others. It isn't a game you play for "advantage". You hope to develop a long term relationship with this institution. Treat them with respect and expect them to reciprocate. 

Don't accept before you are ready, such as when other offers might come in, but don't delay for any perceived "strategic" reason.  

Similarly, once you have accepted the offer, extend the other universities the courtesy of letting them know you will not be accepting theirs.