Hey, only took 5 months to make a proper reply. :/
Anyway, After re-watching the show yet again the only reference to time passing between episodes one and two was a passing comment by Catelyn to Ned (I think, could be wrong but someone said it) about how long the Lannisters have been in Winterfell (which was a few weeks). Then you have to assume it takes another few weeks for the gang (everyone except Tyrion, who is going north to check out The Wall) to travel back to King's Landing. A decent amount of time for the family to get attached to their respective pets, especially children.
You also have to factor in the fact that according to the UK safety laws with using child actors, real wolves couldn't be used so the production team settled on Northern Inuit Dogs (As per Wikipedia anyway). I'm hoping now that the series' popularity has grown significantly, that HBO will give the special effects team enough funding to design convincing direwolves as they become more prominent later.