My wife and I have been involved for many years in showing and training dogs. The phrase "correct breed type" is commonly used to characterize what's intended in your sample sentence. Examples are at the reference link, where my example sentences were also found.

I would use "healthy and active dogs with correct breed type" here. You'll hear dog fanciers use "typey" as a shorthand way of saying the same thing, but I think it's too informal for what your context indicates.

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Note added at 32 mins (2010-07-26 16:10:32 GMT)
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I might use "sound" in lieu of my suggested "active" here.

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Note added at 16 hrs (2010-07-27 08:27:38 GMT)
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"Typeriktige" is not "purebred"; the Norwegian terms for "purebred" are "renraset" or "raseren". See this from Norsk Kennel Klub at http://tinyurl.com/2fuatj9:

"Avl og oppdrett av rasehunder er et viktig fundament i Norsk Kennel Klubs virksomhet. NKKs formålsparagraf (§2, 2.ledd) lyder: NKK har til formål å bidra til å fremme utviklingen av de enkelte hunderaser, av fysisk og psykisk sunne hunder, typeriktige, funksjonelle og sosialt veltilpassede hunder."