Moving and Not Taking Fleas With You?

We live at the same address as our landlord, separated by a yard. They have a dog and cat that have fleas, which caused a huge flea infestation in the yard. We don't have any pets, but in order for us to go into our room from outside, we have to cross the yard. As a result, we had fleas in the room, but already treated it. We are moving next week. I'm really nervous, I don't want to bring any fleas to my new home. We only have these items to bring with us: 2 bookshelves, clothes, bedding (but no mattress), books, and kitchenware. Again, there are no more fleas in our room, but I am really dreading the walk out through the yard.

Please advise me.