Real easy
Step 1
Build your zoo build setup how you want it.That means afterwards including bird trees for large birds,cages for small birds,aquariums for fish,terrariums for snake,turtles,or lizards whatever you may use.
Step 2
Change it to a residential lot
Step 3
May be best to use several sims as catchers these will be sims with the collection helper reward that will gather your specimens.Also if doing fish best to have a sim planned ahead of time with any species being used since fish dont escape your sim inventory like minor pets and birds do after X amount of time.Easy to cheat your sims to get collection helper.They will be placed in your zoo build from step 1
Step 4
After catching and placing your critters in cages etc and are happy with it.Edit town hit "split up household" not evict not move out "split up household" you then take all sims in the split out leaving home vacant.You can delete them once split to clipboard
Step 5
Choose that home while still in edit town change it's lot type to community and then small park
Step 6
Save a copy of your lot to the library
You are done you now have a zoo that requires zero upkeep because community lots are self sustaining.They will feed,clean everything the pets there need.Your sims can visit to watch them and the large birds will fly around the room as normal.Any new game/world you start afterwards just plop down the lot from your library everything will be intact.
Example on a small scale
This is still as a residential lot had my sim put these there about 6 sim hours ago.A yellow Chondro Python and a Yellow Naped Amazon
https://i.imgur.com/Jo2mhLr.jpg
Added this in case you do not know about community lots,every 24 hours a community lot rids itself of dishes,messes,broken plumbing whatever changed it from default.Purposely leaving this dirty plate on a table before splitting my household and turning it community lot
https://i.imgur.com/q9CkEBw.jpg
Changed it to a community lot after splitting my household
3 sim days later had my sim visit the community lot
Happy critters needing nothing
https://i.imgur.com/yUfZvax.jpg
The plate of course was gone as expected,granted was gone later the evening of day turned community lot when the reset happens.
https://i.imgur.com/JPm5hva.jpg
There you go pretty simple have fun.Anything you want to add later after that edit it in edit town add your popcorn machine,barista bar whatever.Save it to library if you like that version too.
Edit: As mentioned large birds love to fly all around a room and get exercise often before relanding on their perch so be sure to give them room.