Take him to the vet anyways, even if he is doing great. This is near and dear to my heart. I lost a 5 month old Yorkie because he ate rat poison and I didn't even know where he got it from. The baby needs a vitamin K shot and follow up. My vet told me some rat poisons can take up to 3 weeks to 'take effect' and that by that point its too late.
I hope and pray that Jax will be ok. It was the worst experience in the world for me to watch my baby throw up blood and die while I pet him helplessly.
prayers to your family and Jax! Just make sure she gets him into the vet for the Vitamin K shot!