This strip sets a couple of precedents all by itself.
First, for a while now, there have been kind of two designs for Snoopy. One is when he's sitting down, where he is a cute, compact little dog. Then other is when he's doing anything else, in which case he'll stretch out into an animal more than twice the size of the other one.
This strip doesn't have any drawings of Snoopy sitting dog-style, which become less frequent as Peanuts continues. The other one, the one depicted here, eventually becomes predominant. It is difficult to think of a beagle so large as a puppy, which is probably why this part of Snoopy's character is allowed to be forgotten. This is a much looser style for the character, which in turn allows Snoopy to become much more expressive and energetic, which fuels the growth in his personality.
Second, this is the first strip in which Snoopy's energetic personality annoys Charlie Brown. Once it's conclusively stated that Snoopy is his, he'll say things about wishing he had a normal dog, but until then it's more like being annoyed at a weird friend (a "Kramer") than a family member. Notable is that Charlie Brown refers to Snoopy as a "person."
The drawings of Snoopy here are very attractive generally. I especially like the ones in the first two panels. The first one is iconic, the second shows him running dog-style, which we don't often see.