They won't receive any single account based pets as the beta account is considered a different account.
The other issue is quite common, you pets aren't missing it's just they are in the old pet tab not the new journal. Any new ones you learn will be account wide, and if you re-copy you pet character over they should unlock after you log in on that character.
This affect any character copied over before pet battles were added in.
At the moment though they have just activated account wide mounts, so it's all a little unstable. I'd wait till the bugs with account wide mounts settle day before worrying. You can't access pet battling yet, so no terrible rush just yet.