As long as the kitty's nails are short and and can't do any real damage to your dog - I would let them work it out (monitoring at all times, of course). It's only been a week - that's not a lot of time for your kitten to a) adjust to your new home and b) realize that dog isn't going to try and hurt him!
Could you try giving treats to both animals when they are in the same room - something like dehydrated chicken? That will keep your puppers in the room (rather than running away scared) and it may also give your kitten the idea that good things happen when he's calm and not going after the dog.
I think there's time for them to become best buds - or at the very least, tolerate each other. I wouldn't panic yet
It took our cats at least a month or so to adjust to Loki when we brought him home.
And your puppers and kitten are so so sweet! ♥