Fixed-wing aircraft would be invented by the 50s at the latest, likely in the 30s
The other answers have covered the ways in which an airplane is superior to a helicopter. But we only know this with hindsight, having invented both.
We must ask ourselves: what would encourage the aviation industry to abandon the local maximum (helicopter) in favor of seeking a global maximum if they didn't know for sure that there was a better option out there?
The answer is: missiles.
Amateur historians of war talk a lot about the tank rewriting the rules of warfare in WWII, but in the sky and the seas, the rules were changed again by the rapid developments of rocketry. Compared to cannons, a missile has far greater range and destructive potential. Post-war air and naval development revolved entirely around leveraging or defending from this new weapon.
A helicopter-focused airforce would find itself blown out of the sky by even unguided WWI era rockets, never mind guided missiles. The ability to hover, while operationally useful, would be a death sentence on the battlefield. Combat between rocket-armed copters would be fast and brutal, encouraging engineers to develop maneuverable craft able to bring rockets to bear against enemy air power, while being safe themselves.
Your first planes would be rocket interceptors
Your alternate timeline branches off too late to prevent the invention of kites and gliders. So it would be a form factor known to your engineers. OTL, liquid-fuel rocket planes were conceptualized as early as 1902, and developed primarily by the Axis powers during WWII. They were essentially a glider with a big rocket attached: the pilot would blitz through enemy formations on one or two attack runs, moving too fast to react to, and then glide home when the fuel ran out.
In our timeline they remained marginal due to their drawbacks compared to conventional airplanes (due to high rate of fuel consumption, the Komet's range was 80km and the Ohka's was half that) and were made obsolete by the invention of the jet engine.
But facing helicopter forces (the Flettner had a measly 170km range compared to the 820km range of a MiG-3 or 2,100 km range of a P-38), rocket interceptors would be much more effective, and their speed would make them untouchable. Even armed with cannons, they could close distance too quickly for a helicopter air wing to react, blast them at close range, and retreat before they could be retaliated against (although it's hard to say whether anything would survive the attack to strike back). The retreating rocket planes would simply outrace or evade any fire coming their way (the Komet's maximum velocity was in excess of 1000km/h, carrying it out of a rocket's practical range in under 60 seconds).
Of course, engineers would quickly follow the same logic as in our timeline, and develop jets as a far better engine type to put on these new "powered gliders", leading to a Cold War period that looks very similar to ours, with jet aircraft as the primary combat type.
Silly Wunderwaffle opportunity: Airships and parasite craft
Since the rocket planes would still have short range, and be untested technology besides, your story's armed forces might be tempted to combine them with something more familiar to them. OTL, all major powers experimented with parasite aircraft during the war, putting small planes on big planes to extend their range. The Japanese even put rocket planes on conventional planes. So there is an opportunity for you to field large rotary aircraft with a few parasite fighters slung under the body (the V-12 could have taken off with the weight of up to 10 fully loaded Komets, and even late 50s designs like the Mil-6 would have been able to carry two or three).
This "helicarrier" would act much like aircraft carriers do in naval engagements, launching its air wing in an over-the-horizon strike on an enemy formation while remaining at a safe distance from retaliation. If the helicopter carried sufficient fuel, it would even be possible to refuel the interceptors for multiple sorties.
Since helicopters are slow and have relatively low flight ceilings, another type of aircraft becomes viable (for countries with large helium reserves): the venerable airship. OTL, they were vulnerable to patrolling fighters, but even 1917 airship designs could fly at 2x the altitude of the 1942 Flettner. In addition to taking over the high-altitude bomber role normally done by strategic bombers, airships could also be used as a carrier platform for these parasite rocket planes.
However, as in OTL, these would merely be a stopgap measure until it became clear that the exceptional operational range of jet planes renders the parasite concept unnecessary.