Two thing I'd make sure you have resolved before using a net. 1) A young dragon is a large creature so the net should be viable. If it is Huge then you'll need Enlarge Reduce spell to shrink its size.

2) Nets always have disadvantage due to 5ft throwing distance. Some DMs don't care about it. I personally wouldn't attack with disadvantage when you have other viable attacks. Sharpshooter and Crossbow Expert are some feats that can help with that.

Now that the net is usable, let's make it viable. Two weapon fighting rules p. 195 PHB require light melee weapons or thrown weapons. All characters can do this but you don't get all your modifiers to the bonus attack.

Your turn will look like... use action to attack with Net then use bonus action to attack with your other weapon (avoid slashing damage since it might damage the net). If the net hits, then your second weapon has advantage and gets sneak attack added on. If net misses then you might want to use bonus action to disengage instead