What antibiotic and antihistamine? No, two injections of an anitbiotic(though depending on the antibiotic) a few days apart is almost never going to clear up an upper respiratory infection in rabbits, if your rabbit does in fact have a URI. All giving too short a coarse of antibiotics does is temporarily knock down the bacteria and once the antibiotic is stopped, if the bacteria isn't completely cleared up then it will just reemerge more resistant to that antibiotic being used again. Orally or by injection may not necessarily change the efficiency of the antibiotic, but that also depends on the antibiotic used. And some antibiotics can't be given orally to rabbits at all or it can kill them.
Medirabbit (medications in rabbits)
http://www.medirabbit.com/Unsafe_medication/Unsafe_drugs_main.htm(unsafe medications in rabbits)
Medirabbit (respiratory infection in rabbits)
I'm not familiar with doramectin being used in rabbits as a common treatment option, though I did read up on it. It's an avermectin of which ivermectin is most commonly used to treat mites(scabies) in rabbits. It sounds like your vet used the lower dosage range, so should be safe, but with a real scabies infestation, that dosage wouldn't likely clear up the mites. From what I read the higher dosage of 0.4mg/kg is needed, and between the use of doramectin or ivermectin, ivermectin is still the most effective and preferred treatment for rabbits. So for future reference if you ever have to deal with a case of mites, I would opt for Revolution(selamectin) as the first treatment choice, and then ivermectin, over doramectins use, if given the choice.
https://www.researchgate.net/public...infested_with_the_ear_mite_Psoroptes_cuniculi
Aside from all this, it's unlikely your rabbit should have any ill effects even if it wasn't a necessary injection, unless your rabbit is one of the rare ones to react negatively to that class of drug, as can sometimes be the case with certain rabbits, in particular ones with dutch genes, vienna carriers, or blue eyed whites(similar to mdr1 gene as seen in collie dogs). But if this was the case then you would have already seen a toxic reaction hours after the injection.
Though I will say that if your vet is just doing the injection preventatively and there are no indications of your rabbit having scabies(fur loss, skin problems), then there should be no reason for a rabbit to be getting this injection. It won't prevent a future case of scabies. This medication will only help if a rabbit currently has these mites. Using a topical spot on like Revolution/Stronghold(selamectin) could provide some lasting preventative protection as it's designed to do so, but not more than a month at most(if even that in rabbits because of their fast metabolism), and definitely not 6 months worth of protection.
MediRabbit (sarcoptes mites in rabbits)
MediRabbit (fur mites, ivermectin dosage info)
MediRabbit (ear mites, selamectin dosage info)