Get a decent pteranodon that can survive one or two hits, but also has enough weight to carry the eggs, use a whip. Whips can grab items for you without u having to go down and manually get them. After you get enough, go to the top of the trench and do what you want with the eggs.
They lose 1 point of food every 15 seconds, so to time how long until they start starving, multiply their current amount of food by 15 and then divide by 60 twice. This will give you the number of hours left untill the food stat reaches 0.
With TLC Update 3 out and wyverns are now breedable, I would definitely recommend getting a 190 high base stat breeding pair ready for the future as I don't see why they wouldn't make Rock Drakes breedable as well.
Obtaining this creature will require you to enter the tek trench where puprle liquid and the nests of these creatures lay past the bioluminescent chamber, there you must steal an egg and raise in a cold environment feeding it nameless venom you can get by killing nameless
The rock drake trench can be found at 57,56 at the area of the map called grave of the lost. Recommend u bring a glider suit and climbing picks and if u have a good tame to fight the drakes. In the wild they can be invisible and can glide in the wild so watch out also wear a HAZARD SUIT it's needed. Lastly there are a lot of nameless in the area so bring a light source. Good luck and ohh it needs to be cold to hatch so air cons