If your world looks like 1910, then everything in it looks like from 1910
Obviously, if you craft your world in a coherent WWI-era fashion, you don't need to tell the reader that the car has a WWI-era look. When you say 'car' and everything else looks like from 1910, then automatically the car in the reader's mind will look like a car from 1910.
I still want to insist that the car looks like WWI-era
Most likely you don't need to. What you need to clarify to yourself instead is: what does the car represent in your story?
You clearly chose such a car for a reason. I imagine that if you are insisting of providing a visual description it is because the visual of the car has a meaning.
Within the WWI-era universe, the car could be synonym with novelty, wealth, speed and progress, but what in this particular car that you have chosen projects these images?
A shiny black livery, which could be compared with the frocks of bankers and contrasted to the mud covered uniforms of soldiers at the front. You could use comparisons like this one to convey the time period, as well as provide a short social commentary.
Noise. The car roars up the street, honks gravely, unlike the squeaking of other cars, and dashes away leaving but a splash of mud from the threaded tires. Such cars during WWI-era were symbols of speed and technology. Refer to its pistons, to the rotating parts, to the metal.
Alternatively, the car has a meaning meant for a modern reader. For instance, objects from the past may carry a sense of dignity, optimism from a time when progress seemed limitless (a steampunk theme), or perhaps the frivolous redundant aesthetics that they used to decorate the most advanced pieces of technology (unlike our habit of streamlining design).
Next, identify the elements of the car that convey these images. Is it the straight slope of the radiator grill, high and shiny, like a merciless grin between the headlights? Or is it the overall shape, like a dashing ebony coffin, with three corpses inside who have not yet understood their fate?
I really really want it to be a 1910 car
Fine. 1910 cars had a few peculiarities about them which may convey the idea that it is not a modern car. They are large, often look like bathtubs, with protruding wheels, which look tall and thin, with one too many spokes and spring leafs for suspensions, unnecessarily soft seats without headrest, a roaring blasting engine, they leave a trail of stinky smoke, and you drive them with goggles, clutching to the steering wheel. The engine is quite bulky, and the windows are square, or slightly slanted, but not curved. Finally, at times the manufacturer would add the year in an elaborated decoration on the water cap, so in your case you could just say WWI-era by giving a date
[...] her eyes fell on the the silver-plated water cap above the grill, with the inscription 'Phantom - by Royal Appointment - London 1910'.