Do community college transfer students have a disadvantage when it comes to graduate school admissions?
Simply having attended a community college earlier in your academic career is not going to hurt you if you have a degree, good grades, good letters of recommendation, etc. from a top program as well as all the other stuff that matters like good tests scores and research experience. Having attended a lower status school is not a permanent black mark and simply will not matter if your subsequent work proves that you are top-notch student and researcher.

Having less research experience than your peers who are applying for the same graduate positions will put you at a disadvantage. Ben Bitdiddle's answer on how you might go about getting that given your relatively shorter period of time at a research university is good as are the answers to many other related questions on this site about getting research experience as an undergraduate.