Against biplanes, Fire Breath is already Good Enough
For an idea of how biplanes typically performed, let's look at the British Sopwith Camel. It had a maximum speed of 113mph, a maximum altitude of about 19,000ft, and was armed with two .303 machine guns. They were hard planes to aim making them only effective within ranges of about 100m. Certain Ace pilots could hit from 200m away, but they were the exceptions to the rule.
In terms of performance, a biplane was very similar to that of many large birds. Certain species of vulchers, cranes, mallards, swans, and geese could fly significantly higher than a Sopwith, and many birds of prey including certain species of hawks, falcons, and eagles could fly significantly faster than a Sopwith. So, it's very easy to imagine a large animal like a dragon having similar aerial performance to a typical biplane.
As for armaments: a properly constrained firehose has a maximum range of about 100m; so, if your dragon's fire breathing structures can create fire hydrant level water pressures, and focus his breath into tight enough of a stream, then a dragon would be able to effectively attack a sopwith from the same ranges that a sopwith could attack a dragon.
Each side may have advantages in certain areas vs others, but the fight should be more or less fair.
But a lot of things got better by WWII...
This issue with this question is that biplanes were already obsolete by WWII. Biplanes were used in WWI when engines were not yet good enough to fly with a single wing design, but as engines got better, single wing planes quickly phased them out due to their greater stability and overall performance. What few biplanes remained in WWII were mostly used for night bombing or non-combat roles where their speed was less of an issue.
So, if we fast forward to WWII, the main british fighter was no longer the Sopwith, it was the Spitfire. The Spitfire had a maximum speed of 406mph, a maximum altitude of about 43,000ft, and it's firepower was about 4x that of the sopwith using more accurate weapons increasing the average engage range to 300m.
This is where your dragons would be in real trouble because no animal can fly anywhere near as high or fast as a spitfire. WWII planes were so much more maneuverable than any animal that even if your dragons had a weapon system to match the range and stopping power of WWII planes that they would have no way of engaging them. Infact, many WWII era planes had belly mounted ball turrets already; so, if humans wanted to slaughter a group of dragons, they could just use their superior speed to kite them into the upper atmosphere, and once the dragons could clime no higher, they could just fly circles over the dragons picking them off by shooting down at them with their ball turrets.
The accepted answer will fail your dragons because your baby dragon "missiles" will likewise not be able to reach the heights or speeds necessary to catch a human WWII aircraft.
So for your dragons to beat WWII tech, the question is less about what weapon they use to attack the human fighters as how they fly fast and high enough to engage them at all?
My first thought here is to strap a jet engine to their backs. Jet engines were invented in 1930, but WWII eneginers struggled to make them a useful technology because designing a stable fuselage becomes much harder at those speeds. Dragons can skip on the fusage problem because a dragon is a living thing which can reshape its body based on the forces it feels. This would mean that dragons could use the technology of the day to fly faster and higher than WWII planes allowing them to quickly close into distances where they could use their shorter ranged weapons on their enemies.
But since the OP asks for a magic solution, just replace "jet engine" with "magic flight enhancement". I imagine something along the lines of dragons tattooing themselves with some kind of runes that allow them to fly much faster and higher than their biology alone would imply or something like that.
You could also invert the equation by giving the dragons a weapon with enough range that the faster human fighters would be forced to close the gap to engage the dragons up close, but this weapon system would have to be able to shot up from the dragon's maximum altitude, to the human's maximum altitude which is probably somewhere on the order of 10,000-20,000 vertical feet. This would be much harder to balance since any weapon with THAT much of a range advantage might give the dragons to much of tactical advantage.