Is what you have one of the dairy-free formulas? Rabbits are lactose intolerant, so if it's not a dairy-free formula, I definitely wouldn't give it. Also, do you have a full ingredients list you could give us?
It's pretty difficult to overdose with probiotics - underdosing is a bigger concern. That said, BeneBac Plus has 20M+ bacteria per gram, with 1g being the dose for rabbits up to 10 lbs; the stuff you linked comes in capsules with 30-50 billion, so it would take *very* little to get an adequate dosage into her but at the same time, a little extra shouldn't hurt as long as it's safe to give her the product in the first place. Without knowing which formula you've got and the exact ingredients for it, though, I'm not comfortable wagering a guess one way or the other.
I second lovelops' suggestion about calling the vet and confirming it with them - I see no reason why probiotics would interfere with any other meds, but I'd trust a vet's opinion over my own regarding whether or not the product is safe to give at all and how *much* it's safe to give if it is.
Anyway, I'm glad she's improving a bit - sounds like you caught things early and she's got a good chance of making a full recovery!
True diarrhea, which is very watery, is a medical emergency. You said "a little diarrhea" though, which makes me think it's loose stools rather than actual diarrhea. This site shows the difference:
http://imgur.com/a/5N4lD
If it's loose stools, I'm inclined to blame the Nutri-cal, which I honestly don't think is safe for rabbits. It's nearly 30% fat and it appears to be designed for cats/dogs (unless there's another formula I don't know about?) which means it probably contains things rabbits aren't able to digest, seeing as they're vegans.
I would stop the Nutri-cal ASAP. Get some Critical Care if you can (apple-banana flavor - bunnies tend to hate the anise, though my vet says it's popular with guinea pigs). If you can't, then feeding a pellet slurry would be far better than Nutri-cal. The difference between Critical Care and powdered pellets is basically just that the Critical Care has extra nutrients added to it. It's definitely better if you can get your hands on it, but pellet slurry is a perfectly viable substitute if you can't.
Pellet slurry is easiest to make if you have a coffee bean grinder, mortar and pestle or perhaps a food processor that you could break the pellets up with first... however, if you don't, that's ok. Grind them up if you can, then put the pellets (or ground-up pellets) in a bowl; add enough water to cover them + a little extra and microwave them until the water boils. Leave the bowl sitting on the counter for 10 minutes or so, to give the pellets time to absorb the water. Break them up/mix it together as best as you can. If you don't have a grinder, you'll definitely need to cut the tip off of a syringe and widen the hole a bit before syringe-feeding the slurry so that it can get through the syringe.
As for the blackberry puree, you wouldn't want to give too much fruit since it's so sugary, but you could add a little bit of puree'd fruit (or fruit-flavored, preservative free baby food) to the slurry after you made it and you could also include ground-up hay in the slurry if you had a grinder.