You may want to wait a bit on the pellets until you get the mushy poop sorted out. Adding in new foods when there are already mushy poop problems, can often contribute to the issue and the microflora imbalance. Especially if cocci is causing the mushy poop, then hay really is the best thing to help restore the gut balance. Once you get the mushy poop cleared up and the poop has been normal for at least a few days(may need longer though if it comes right back), then you could gradually start adding pellets in if you want. You may want to try and find a probiotic to help restore the gut balance as well. Common ones used for rabbits are Bene Bac or Fibreplex, not sure what you have available to you though. Also wondering what type of grass hay is it that you are feeding him?
There is debate whether pellets are good or not. The reason is that the carbs and sugars in them can sometimes lead to digestive issues developing, especially in rabbits that have an extra sensitive GI tract. I've had a rabbit that couldn't have pellets and was on a hay/veggie diet, but I also feed my other rabbits limited amounts of pellets in addition to their hay. The reason pellets can be a good addition in a rabbits diet is because they contain a balanced amount of the correct vitamins and minerals that rabbits need. So a bit like a multivitamin. And as long as a rabbit has a healthy GI tract and doesn't have health issues that make them sensitive to pellets, then pellets are usually fine to have in a rabbits diet. For rabbits not fed pellets, it can be difficult finding the right balance in their diet with veggies/herbs/forage, but it is possible.
When picking a pellet out, you really want to try and find one that has alfalfa hay as the first ingredient for baby rabbits as they need the higher protein, and for adult rabbits I prefer a pellet with a grass hay as the first ingredient as they are usually lower calcium, which I want for my adult pet rabbits. Then you don't want too many grain ingredients, and you want grain and sugars to be as low down on the list as possible, definitely you don't want a grain product as the first thing on the list. I also don't like corn to be in the feed at all. I like Oxbow rabbit food, and I believe it should be available to you there online, in pet stores, or your vet should be able to order it in. They have a young rabbit food and an adult food. Hay is the first ingredient in both and it has a higher amount of vitamins added to it, which is good when you are feeding it in limited amounts along with unlimited hay. I know a few other RO members from Australia, also feed their buns Oxbow. If there is another feed that you are interested in but aren't sure about, you can always post the ingredient list on here and we can give you our opinions on it.
When adding pellets into the diet, you want to do it slowly like you do with veggies. Start with a small pinch of pellets for a couple days, then gradually increase the amount over a couple weeks if there are no signs of digestive issues. You want to be feeding close to unlimited pellets. I will usually feed baby rabbits twice a day and just enough pellets so they run out about 3 hours before the next feeding, then they can snack on their grass hay. I've found this makes sure they are also eating enough hay for good gut motility. Basically you want them at least eating a pile of hay the size of their body each day and then the rest of their diet in pellets. If you are seeing fecal poop that is smaller than it should be, hard, dark, and may be sticky or irregularly shaped, then the rabbit isn't getting enough indigestible fiber from it's hay and it needs less pellets and more hay in the diet. You want a rabbits poop to be soft and crush easily in your fingers. If you start seeing mushy poop again, you may be increasing the amount of pellets too quickly or the bun may not be able to tolerate too many pellets in the diet. In which case, reduce the pellet amount until the mushy poop stops, then more gradually start increasing again. If you again see mushy poop, reduce pellets until it stops and then you may just need to maintain pellets at the amount where you no longer see mushy poop. If you ever see watery diarrhea, that is different and you should stop pellets, continue with grass hay, and contact your vet immediately. This link gives a good explanation of the different types of poop you might see from your rabbits.
http://imgur.com/a/5N4lD
There is also the added need of baby rabbits, for higher protein and nutrients while they are growing. And it's a good alfalfa based pellet that usually will provide these needed nutrients. When feeding a grass hay only to a baby rabbit, this will usually slow their growth rate because of the lower protein and nutrients. Once you are able to add pellets into the diet, if you find they are causing digestive issues for the baby, you could instead try adding in alfalfa/lucerne hay into the babies diet. This will provide it with extra calcium and protein for growth, though just not as balanced as a pellet would be, but also doesn't have the added grains and sugars that pellets have and which are usually the triggers for digestive issues when they occur. If you do add alfalfa hay into his diet, just make sure to do it gradually over at least a week, as rabbits digestion needs time to slowly adapt to new foods(aside from grass hays). So start off with a small amount and if it doesn't seem to cause any problems, gradually increase.
Until the baby rabbits cocci problems have been confirmed to have cleared up, I personally wouldn't let your other rabbit be in the same area. If your other rabbit had an overgrowth of cocci, you would probably be seeing symptoms of it, but sometimes you won't at first, so if you have any concerns you may want to have a fecal test done to confirm your rabbit hasn't been infected. I found one rabbit vet listing for Tasmania. Not sure if it is current or even how good the vet is, but it is under rabbit vet listings.
North Hobart Veterinary Hospital
Dr Rupe Woods273 Elizabeth Street
North Hobart 7000TasmaniaPhone: (03) 6234 7044