Either:
A) She's been planning and working on adopting another dog since Theo died, and has been fortunate that the stars have aligned and it all worked out to happen very quickly. In that situation, she's lied that she's only been considering it for the last 48 hours.
B) She has skipped the queue to adopt a dog in record time, and in circumstances that most rescues wouldn't re-home to (having 2 under 5s). Her celebrity status has almost certainly helped speed up the process and bend the rules for her.
C) She's bought a puppy and lied about adopting.
Either way, her "I'll update you after the school run" means "I'll update you through a series of spaced out stories followed by a grid post at 6-7pm for prime engagement".