It's going to be really hard to experimentally determine the invasiveness of a species - there are just too many variables involved to be able to adequately control them all.
Also, it's going to be difficult to do a short-term experiment involving aquaria, as just getting properly cycled takes about a month, and many of the critters have a lifespan that would make it difficult to study population/breeding and what not.
If you are set on the Asian carp, maybe look at some of the reasons that people have given as to why it's been so successful as an invasive, Or maybe just comparisons with it's original environment, and what natural limits it may have (disease, predation, limited resources) that aren't limiting in North America. Though, it will be more difficult to use the scientific method; I wish the educational system wasn't such a stickler on that, it's really just a tool/guideline.
If you can deviate at all from the Asian carp, maybe try something involving algal growth with different substrates/conditions, or the rate of population growth in daphnia (or some other live food culture) based on different food types or something.