As a secretary myself, I think she is way out of line. I'm responsible for booking all of my boss' travel - last minute business and all of his personal travel. That's what we, as assistants, are here for - to take care of the details and deal with the headaches associated with making last minute travel arrangements, amongst other things. As long you are not a choosey beggar (unrealistic expectations - flight times, connections, etc.) then she shouldn't have any comments. When it comes down to the wire, you might not end up with an ideal itinerary due to limited flight choices/availability at the last minute. Just remember it's not her fault if the flight you want is sold out.
Try explaining to your assistant that you would like to give her more notice about your travel plans, however you don't have that option sometimes. She should understand and deal with it. If she keeps complaining about it, then she shouldn't be a secretary. We are here to make your life easier and take care of the penny-anny stuff that sucks up your time. That's why we're called assistants.
Heck, I have my boss ready to take mileage runs to keep his elite status. I'm in charge of maximizing all miles and bonuses for him and his wife. He's even willing to let me route him through funky connections so he can obtain the mile bonuses associated with specific routes. He frequently asks for printouts of the spreadsheet I made to track his miles.
Now, you might be right about most secretaries not understanding corporate travel, however I don't appreciate the blanket statement. I'm not flaming. Just defending my profession. I don't think your secretary understands her job description, let alone making travel reservations.