Hi Gem,
Welcome!
I think your dream was showing you that the dog is still here. Maybe the dog is still hanging around to say goodbye and make sure everyone else is ok. I think this is common, and I don't think it means that the dog's spirit is restless and lost, but just making contact.
When I had to have one of my cats put to sleep due to severe sudden diabetes, he visited me the very next day and continued this for 2 months. It started because I was crying, missing him, so badly and I felt him jump on the bed and lay down. He had always slept in the middle of the bed while alive, and this is what I felt continue after he died. There was only one time where my husband and our other cat felt it too (which is when my husband finally believed me) and we both decided to let him know we loved him and that if he needed to move on it was ok. While I wasn't sure if he was stuck here, it didn't feel like that to me. I think he was just there to comfort us. Anyway, we didn't sense him anymore after that.
And I've heard several people tell me the same kind of stories with their own pets! I think our pets just really care about us and want to check up on us.