It can be done. I changed a 75 Duster to a 70/71 Duster front end.
Besides the grill you will need an upper and lower grill support for the new grill. ....a Hood to fit it...and bumper....
Not sure if the bumper mounts on the frame are the same for a 73....but my 75 had to to drill holes in frame to mount 71 bumper...no big deal....
also on the 75 Duster the i had to make a small tab and weld it to the fender as the new fender is missing one on the mounting bolt tabs for the upper support.....
Some of it depends on the year and the model. The Dart's don't have lower grille supports, just the Duster's. But the '70-72 Dart's had valances. His car being a '73 should keep him clear of drilling any holes in the frame because he should have a non-shock mount bumper. Just depends.
I swapped my '74 Duster over to a '71 Dart (Demon) front end, but my '74 was the change-over year for shock mount bumpers, so my car had all the mounting locations on the frame already.
This shows the front frame rails, the "standard" rail is the non-shock mount bumper and they all used the same mounting locations. Then there's the shock mount bumpers, which are a little more complicated than what this shows.
With the '74 cars they started with shock mount bumpers, so, single mounting hole like the bottom one above. Then at some point, like December of '73 for '74 model year production, there was an issue getting shock bumpers. So the factory went back to standard brackets. So my '74 ended up with a standard bumper and mounts, but also has the provision for the shock mount. '75 went back to the single mounting location.
But beyond the shock mount bumper thing, you can swap pretty much any front clip on an A-body except the Barracuda. Scamps are just Duster front ends on a Dart, Demon's are just Dart front ends on a Duster. Valiants were an early Duster mash up with "Duster" fenders and their own grilles, hoods and filler panels for '67-69. But all the body lines from the Darts, Valiants, Dusters, Demons, Scamps and Dart Sports all line up at the doors. So if you take everything that unbolts from the doors forward you can swap it.
Like this example a Duster with a '67 Dart front end (not mine!)
For the OP's car, being a '73 with the single piece fenders already, the '67-69 Dart front end would be the fewest body panels to go find. Duster/Valiant/Scamp would take the whole front clip. '70-'72 Dart would take either the whole front clip, or some fabrication to make the '70-72 lower valance bolt to the '73 fenders. Where the '67-'69 would just be the hood, hood latch panel, grille and bumper. It is possible that the '67-69 grille could even be made to work with that modified '73 hood. So if you could find the grille and bumper, and be willing to do some extra work getting the grille mounted, you might be able to keep the hood and latch panel. But you still wouldn't have any front trim options for that hood.