The "Ideal system" for heating and cooling a home is to have the heat source closest to the floor, and the cooling source closest to the ceiling. Basically, this is because hot air rises, and cold air falls. Due to the added expense of essentially having two systems in one house, most houses have only one system. In your case, you will have two, with the hot water system at floor level. From a comfort standpoint, the AC ducts should be at the ceiling. Having said that, of course, does not solve the issue with your daughter.
One point about your AC system. Most of these systems have two sets of ducts. One set, what you are calling vents, supply the heated air into the room. The other set, the return ducts, remove the warmed air and run it back to the ac unit to be re-chilled. Ideally, when the supply vents are placed in one location, lets say, top of the wall nearest the ceiling, then the returns should be at the opposite location, the bottom of the wall nearest the floor. In this case you might have the same problem no matter where the vents are, although usually you also want the two vents to be at opposite sides of the room as well.
First, find out about different filtration systems you can add to the ac unit, and discuss them with your allergists. My wife suffers terribly, and our solution (from her allergists) was to install an electronic system to scrub the air. It was about $350 installed, but of course we need it for winter as well as summer. If you could go this route, you could locate the supply vents in the ideal ceiling position.
Second, find out from the allergists if you can have the supply vents slightly off the floor. Typical baseboard radiant heat is about 6 to 8 inches high, and there is no reason from a building standpoint that the vents could not reside just above the baseboards. This would require some slightly different construction techniques, including possibly making the walls thicker so that the vents can be insulated properly. But this is a viable solution.
Third: there is no reason that the baseboards could end on each side of the ac vents. Like above, though, this would require extra work as the hot water plumbing would need to be routed under the floors wherever the vents were, adding to the cost of construction.
Fourth, consider having the ac supply vents in the floor instead of your toe-kick position.
Fifth, you may want to consider radiant floor heating instead of baseboard radiators. This means that the whole floor becomes the heat source. Although I have no personal experience with this kind of system, it supposedly is very good. It may cost more than baseboard, so one possible alternative is to just do your daughterís room with a radiant floor system, and keep the rest of the house with baseboards.
Other general suggestions:
Request that the ducting material NOT have the insulation material on the inside of the ducts. This keeps the inside of the ducts smooth, thereby reducing a place for bacteria to grow. After the house is built, have the vents power-cleaned to remove any construction dust.
Eliminate, or at least limit wall-to-wall carpet, for the same reason as above. Throw-rugs are easier to clean and therefore do not collect allergens as easy. A hardwood floor or wood laminate can often be very comparable in price to carpet, and very durable.
If you are planning for fireplaces in the design, do not use vent-less. Although I prefer a real wood-burning unit, gas is usually better for allergy sufferers. As a compromise, I do not use scrap-wood kindling, and opt for those manufactured logs, which has helped my wife a great deal. A wood stove can be good, too, if you like them. Whatever you choose, make sure the unit has itís own outside air supply. Your contractor should know exactly what I mean.
Last, consider a whole-house air scrubber no matter what else you do.