Should I be suspicious of a conference that invites me, a recently admitted graduate student, to be an invited speaker?
It seems it is a junk conference, which will not bring you anything, but waits for your money! 

Don't go, it is a waste of time, you will get nothing good from it, since no one really involved at a high level in your field will come.

It is not unusual for those kind of conferences to invite "anyone" as an invited speaker.