My boyfriend and his ex still talk and share the dogs they had together. Help!!?

[Gemma]

We have been seeing each other for 4 months now and he was with his ex for 9 years!! They have 2 dogs together and she still calls to see the dogs and see how they are. They are still sorting things out as they had only been split up 4 months when i met him. He has told me recently he loves me and he would never want her back. Im beginning to struggle though with how im feeling when she telephones and i dont know whether im being silly and insecure or should i just dump him and move on to meet someone without an ex still floating about. Any help is much appreciated. Thank you