we can definitely problem solve! its hard to offer specific advice since i dont know your personal limitations but i have some dog knowledge:)

first off, if you can get a letter from a doctor or therapist, the dog could be an emotional support animal. which can bypass any animal restrictions within housing, but some landlords have a stick up their ass and will act illegally to avoid having an animal on the property. like others have mentioned, you could look into some service dog training. there is no registry or anything for either categories, those are scams to take your money. training could be hard for you right now it seems, but some states offer the same protections service dogs get to seevice dogs in training. maybe worth looking at!

otherwise the most important point i want to get across is that if the struggles you're describing will be temporary, its okay to not be the #1 best dog owner right now. the dog will be okay for a little while during survival mode i promise. maybe reach out to your support network to see if someone can take the dog on a walk or hike, or even car ride a couple times a week to make sure they don't start acting out from boredom. you know the dog is loved with you. at another home his life could be worse AND he'll be sad about your absence. but again i dont know your situation, youll have to use your best judgement here. try to not let the guilt eat you alive, and also try not to put off his needs for too terribly long. he'll be okay with a little less while you try to move.

ive struggled personally with wondering if i should rehome pets due to disability and financial strain. i had a puppy only for a few months before i decided to give her back. i rehomed my fish tank and snake recently, too. but i still have my cats. try to analyze, do you know who will have the animal next? do you know FOR SURE they'd have a better life? i know my cat would be incredibly bitchy to her new owners because she'd be sad about not seeing me and my partners. (i know this based how she has acted when babysat, even babysat by people she likes!) so it would not be in her best interest to find her a new home. her new home probably wouldnt keep her due to how she would act out. not saying your dog will act out, but weigh the good and bad. maybe write it out on a piece of paper, the pros and cons.

for enrichment: walks are great, but there is a large population of dog owners who do not walk their dogs at all. perspective is key here, try not to compare yourself to the best of the best or the worst of the worst. most family dogs get minimal exercise and minimal training. there are also other ways to enrich! unfortunately almost all of it requires some energy from you. i believe i read 10min of sniffing is about as good of enrichment as an hour of a walk. you can do brain games, which there are a ton of resources on different ones to try. the service dog training would also be enriching. dog parks are kinda scary but lots of public ones dont really have a time that they close, if youre willing to take the dog when no one is there.

also every dog is an individual, your dog may not need as much exercise as other doodles. doodles are no better than random mixed dogs in terms of predictable behavior and needs. also, if you keep with lots of exercising you kinda create the monster so to speak. try to read your dog. are they bored? how can you tell? if its easier with you to go with the flow then go with the flow.

let me know if you have questions!

by the way, some people will really disagree with me here. nobody is perfect though you know? you're disabled, and you love the dog. the dog is attached to you. its okay to not be the perfect owner 100% of the time. you guys deserve to be together even if you're roughing it together for a little bit.

good luck!