I'm just wondering if I should be worried or not on this.
Neither of my previous dogs did this (they were adopted as adults) ... my little guy has a favorite stuffed toy - a fuzzy ball - and he will walk around with it in his mouth and whine -- we've had him just over 6 months and he's a bit over a year old now and this has started happening in just the past couple weeks.
If it matters, he is a rescued beagle-jack russell mix. We don't have other dogs so its not like another dog might take it. We do have cats, but they don't go near the dog's toys.
My husband & I can take this or any of his toys away from him and he is not aggressive or protective.

Just wondering if anyone else has seen this whining with a toy in the mouth and if I ought to be worried about it.

Sometimes he will just walk around with it whining, not trying to get my attention to play.
He knows if he wants me to play with the toy that he brings it to me and drops it and that I will pick it up and play with him (we've been trying to master "drop it" so I make him practice with toys when he wants me to play with him).