Firstly, I think its reasonable to say that pain in general not just from sex with animals is taken differently by everyone and being proactive and working towards making things easier to take is the best thing you can work towards. Stretching yourself to be able to take something larger than the knot of said dog is a very good idea. If you can get a toy (lets say seven inches in girth because that is my personal experience with stretching and limits), or even your own fists to fit inside of you doing that occasionally will get your body to the point where it is comfortable to stretch and stay that way for the duration of a tie.
Secondly, kill any anxiety you have in your mind because sex with animals is fucking great <3 relaxing, enjoying a little doggy foreplay (in whatever healthy variety you like it, I prefer lots of kisses and licks myself hehe) is a good way to get your body to chill out without needing the use of any drugs, stimulants, or outside influence (thought having someone to spot for you is a good idea). Take things slow and have a good time <3
Lastly. Do not use pain meds, poppers, uppers, or stuff to dope you out. Especially for sex with an animal that is (im imagining) packing heat WAY larger than a humans. Its a bad enough idea having anal sex with a human and not feeling the possible pain that there is during something bad happening. If your body is going to feel pain it NEEDS to feel that pain to alert you as to what is going on. You don't want to have an entrance tear, bad angle, or even a prolapse and not realize it until after you've finished screwing for an hour. (or several ;3 ) Just my recommendation I know some people do not have the largest pain tolerance so its understandable to want to have some sort of barrier between your ass and something maybe a lil too large for you, if it is truly an issue of pain I would recommend THC edibles or just toke up on some weed and don't go for anything that could put you to sleep or overstimulate you.
Best of luck and i hope you have a good tie!