I know there's already like 1,000 of these tips but here's another with some extra info that I really wish I knew earlier! Keep in mind I still play ASE.

So first you need a light pet and a hazmat suit, basic stuff I won't get into. Find a high level reaper queen, I like to search specifically around the edge of the radiation zone so I can kite it into non-irradiated blue zone and wear better armor, then make a trap nearby (I highly recommend captain fatdog's/at least using double doors, and making sure that all the foundations are all decently above the ground).

Next, you're gonna need to go find the reaper queen again and kite her into the trap, then damage her until she's at less than 2,000HP, I recommend turning off your light pet (can be done through emotes in the whistle wheel!!) to do less damage when she's really low to reduce the chance of accidentally killing her. Then she'll glow pink and you can stand somewhat close, next to your PASSIVE tame so you can be climb back on when she's done. When she unaggroes to the trap, if you're standing in the sweet spot where she can't attack but she can still aggro to you, she'll crouch down with the little spines on her head twitching (If she doesn't do this, you're probably about to get knocked out, climb back on your tame), pick you up and impregnate you.

If you're doing this on a server with high growth/gestation rates, you can be impregnated multiple times with a box nearby to get multiple reapers with slightly different stats. If the queen gets out while you're leveling up, you can pretty easily trap her again if you chose a flat area. I managed to get one reaper with 24 melee and another with 30, plus 1 reaper with 35 health and another with 39. (For ASA you'll probably get much better stats since the speed stat was removed.) You can also drag out any friends or tribemates if you're on a server with lower gestation rates.

For the baby, I find that a 1x1 box works fine. If you have the Dino Storage mod/The ASA equivalent you can use the soul gun to easily pick up the baby, or fill your inventory with cooked meat and let it kill you (better on lower rate servers/officials).