To move to HCMC with pets (Ho Chi Minh City)

Hi,
I was wondering if any of you had a personal experience on moving to HCMC with pets ( cat in my case ).
Sadly, I haven't read confirming comments on a few forums.
My questions would be:
1) Is it easy for them to enter the country? Is there any quarantine required?
2) Are they allowed to live in rented flats / apartments?
3) Are they respected overall? I don't want him to end up in a restaurant menu..

Thank you in advance!

Best

E