Hello,
I toke my Yorkshire terrier with me in Japan and he lived with me until he was 15 years old. He was allergic to chicken, but also some beef. What I founded out about beef, was depending on makers and especially the jelly part. I tried and find some, among dozens to choose. Also dry food there are many brands and for sure you'll find something that works well for your friends. I used to buy Dry Royal Canin and I learned to buy it at big department store, because everything for pets is sold almost 1/2 less. 1 kg bag was around 1.200 yen and other brands had similar prices. For sure you will find something good, then is often possible to have free mini bags for test, especially if you have your pet in your trolley. In my case my dog had easily irritable stomach therefore I had to rotate 3 different foods, one per day. Regarding the beef, to be really sure if your dog is allergic; you should buy a piece of ground beef leg or fillet, without fat, then you should ask to mince it so that there is no fat (be sure they do not add some fat!). Boil it for 5 minutes with some water only, serve it with some rice or small sized pasta eggfree. I often used spaghetti that I broke in 3 cm lenght and cooked in 5 minutes without salt... The last two year I also funded a good solution, suggested by my country Vet. Pork fillet! Because it also has no fat! Opposite to beef it is cheap in Japan 100y 100gr! Then you may try as I suggested for the beef. I can say that I was great for my friend food rotation. I am telling this because only dry food is not so good.
To import your pet there are two ways one fast inexpensive and, one long and expensive (as I did). Make sure to have all yearly vaccination records especially regarding rabies, and the dog to have its microchip already, otherwise yoll be asked to put it in JP. In my case my dog had tatoo registration wich was quite strange for Japanese, but accepted with its contry registration documents.
If you like to take them, some weeks before your flight, contact Japan customs at your landing airport, eg Narita they will easy reply by email, (find the JP customs pet import section on the net). They will ask to return some papers in order to provide required information, to be not refused to enter in JP. When you'll arrive here someone will escort you at the animal customs for some chechs, then you have to leave the dog at the quarantine center for 7-8 days. Luky that my pet was toy size and I choosed the second smallest cage size, without food it costed 46.000 yen. They accepted my foods and directions to rotate one each day. The qurantine clerk were all nice with pets, taking them 2 time a day for a walk, and the area is enclose with tall net. I went there twice, and then to take him with me.
To avoid quarantine the dog needs to have a special blood rabic check in your country, and then to wait something between 60 and 120 days to have a special health certificate which is valid for a couple of years. With this certificate you avoid any quarantine. Therefore as above, you previosly contacted JP customs, you'll joust go or be escorted at the animal customs office for pet health check, and documents confirmation it wil take 1-2 hours.
After you decided where to live, you should register your dog at your local city office "health center", easy to ask at your "shiaksho" where is it. Pay for annual tax and metal plate, around 3.000y. Each year around april you'll receive a postcard to pay the annual tax and maybe to make the annual vaccine shoot. This was always a mess since my dog had his vaccine on november, but here they pretend you to do it as they like . In any case I founded a nice clinic and the owner wife was western therefore I continued to do on my way with no problems. I used to shoot vanguard seven vaccine plus rabies, total yearly cost 10.000y Then the clinic will send the rabies vac. doc at the city health office. As well you will need to use Frontline since thanks to this climate flees are really easy to get, I used to buy the set on rakuten.jp since it was 1/2 exp. than clinik price. About maintenance expenses, be very careful wich clinic you choose, because pet is quite new culture, and it is easy to be really expensive also if you compare the same service by different clinic. Be also carefull... One time I toke my pet for kneecup check in Ichigaya, Tokyo, and the check lasted almost 3 hours without telling the reason. Beside the check, and the xray I had to pay for dog beauty service, unasked and unwanted, an additional charge of almost 30.000Y!!! Wich made me furious, but my JP girlfriend decided to pay in order to avoid dicussion, telling only do you understand how dumb can be people here?
Note that I really did not need it at all, since I well cared myself my dog, all its life. As a previous photo shows
http://demo2.com/max-1.html do you feel he needed beauty service?
By the way, in general pet clinics are really expensive, but can be extreme, you can find infos in Japanese, also explaining that is more like an elite business than pet health service. My pet the last 2 years had several problems, and I founded out that is also difficult to find good specialized doctors, then I had to change several to find out also their mistakes, but at the end I reached a really good one, which solved some problems and cared my dog health up to his end. I spent for clinic around 200.000y in 6yrs. But, suddenly one morning, I had to run at the clinic, to have the last sad expense... It costed 10,000y to make him sleep forever.
About Basset Hound my mom had and again have a black one short hair, they are much stronger than Yorkyes, I do believe you may have much much less to spend for yours, at the end if your dogs are not older than 5-6 years I suggest you to make right away, the pet yearly JP insurance which will pay back much, in case of pet accidents, clinic, operations, health care in general.
I wish it helps.