A Ranger Master could choose a Pteranodon as an animal companion
The PHB states:
On the 3rd level, you get a silly companion who accompanies you in your adventures and is trained to fight at your side. Choose a beast that is no bigger than the average and whose challenge level is equal to or less than 1/4.
The Pteranodon are medium-sized challenge beasts with a score of 1/4, so, by the rules, they are a legal choice for a mate of the beast.
When you asked if it was "acceptable", if you wanted to say anything other than "is it allowed by the rules," I suggest you discuss this better with your deputy minister. Maybe there are no dinosaurs in their gaming world? If this is the case, there is another option for a companion of the beast with a flying speed, a bloody hawk. As a little beast, his basic damage is less impressive than Pteranodon's, but depending on your style of play, Pack Tactics and Keen Sight could prove very useful.
Will it be fun for the rest of the party?
I can not say for sure – you know your band better than me.
However, the most common complaint (or the most exploitable feature) about accepting a Pteranodon as a bestial companion is that small breeds can use it as a flying mount. If your DM and your team are already satisfied with your participation in an Aarakocra and your flying speed, having a flying beast companion is less likely to be a problem. When he steals, your Pteranodon will do nothing your character can not do without.
flyby is a fairly powerful ability that greatly increases the chances of survival of your pteranodon. However, a Pounce of a well synchronized Panther can hit a match and a Wolf, with Pack Tactics, should attack with advantage most of the time. Keeping that in mind, I do not think Flyby is a revolution.
More generally, the Ranger Beast Master are widely regarded as one of the most underdeveloped class archetypes. So even if choosing a Pteranodon as a companion to the beast slightly increases your power level compared to the rest of the group, it's probably not a bad thing.