There are several issues with that:

• we didn't see Bronn dipping the spear in poison. And they couldn't be pre-dipped because the poison would dry up. And dry poison loses its potency;
• the spears didn't have any kind of injection mechanism, to assume they had a poison reservoir that injects on impact. We don't know if Westeros even has that kind of technology;
• such a small quantity wouldn't work on an animal that size. Dragon is the size of an airplane. And in poisons, the size and weight of a victim is very important. Use too little, which would be the case in this situation, and all you do is irritate the wound and nothing more;
• you wouldn't know what poison to use because nobody has even seen a live dragon in over 150 years, let alone one the size of Drogon;
• we don't know if poison works on a dragon. They're magical creatures;
• why would you put emphasis on showing the Queen your new scorpion can pierce dragon bone, if you're going to use poison? You don't need to shoot a spear into his brain for that;
• the Dornish are known for using poisoned weapons (see Oberyn Martell). And they never poisoned a dragon. Are you saying they never thought of poisoning Aegon's dragons during the First Dornish War?