How long will it take to go through security at Brussels Airport

The "direct train to Amsterdam" departs from Brussel Zuid (Bruxelles Midi) station, not the airport. Trains run very frequently downtown, however.

It doesn't take particularly long to process through the airport. At that time in the morning, before most intra-Europe flights arrive, probably about a half hour.

Now, the nasty surprise regarding your Eurail pass, other than the fact that it's a waste of money for Belgium and the Netherlands (and most other countries as well). The direct train between Brussels and Amsterdam is operated by the multinational consortium Thalys, and they limit the number of passholders who can ride each train and require you to pay a hefty supplement.

My preference would be not to book ahead for this reservation, given the airline arrival and processing issues. I would probably accept one extra hour travel time and one extra connection (Airport-Mechelen-Rotterdam-Amsterdam) to avoid paying the Thalys reservation fee (39 euros in 2nd class or 55 in first, with a snack served). It's easy enough to hop on all those trains, after activating your pass. This is also your back-up plan if you activate your pass in the station, ask for a Thalys reservation, and are told that places are sold out for passholders. (Also, looking at our Rail Europe reservation link today, I'm not getting accurate results for Brussels-Amsterdam passholder reservations.)