Can I replace a complementary N&P channel MOSFET with two separate MOSFETS?
Can you replace it with two discrete mosfets? Yes.

Should you? Much more difficult to answer. The pre-packaged duo has been matched so that the turn on and turn off times are similar for each. That SMD package would suffer less parasitic inductance than a discrete pair of mosfets. So far that has two things going way for it, as matching devices is difficult and not guaranteed to happen in the same batch of discrete transistors you buy (There are also fewer discrete mosfets that are made to be compliments to each other than there are BJT's, not quite sure why, but that's what I've seen.). The parasitic inductance really can't be overcome as it's a product of the packaging. Pretty much the only reason I'd ever not replace a part with it's identical or equivalent competitor's is if the product no longer existed. If you choose to go the discrete route, then please ask for help in selecting mosfets that meet your LCD's criteria in a new question, as that is a whole can of worms on it's own.