The standard queen size bed measures 60 inches in width and 80 inches in length. A standard full size bed measures 54 inches in width and 75 inches in length. In terms of your headboard, the only measurements that will really matter are those for the width of the bed. When you upgrade to a queen size bed, you are gaining an extra 6 inches of width across the head area of your bed.
The first thing to do when you are figuring out how to make your old headboard work with your new bed is to measure the headboard. If your headboard measures more than 60 inches in width, you should not have any problem using it with your queen size bed. If your headboard is smaller than 60 inches, you can still use it, but you should be aware that part of the mattress will extend past the headboard on either side of the bed. This disparity should not be extremely noticeable in most cases.
To make your new queen bed work with your full frame, you will simply need to position the bed frame so that it is centered within the headboard. If your frame bolts or screws into the headboard, you may need to create more holes or move the brackets that previously held the frame in place, so that they will allow enough room for the new bed. There will be less room on either side than there was previously, but that should not pose a problem with the majority of beds.
You may run into a problem making your headboard work if it is not made out of a solid material. In this case, you may have to fasten the headboard to the wall and then place the bed frame in front of it. Conversion kits are available for some beds, allowing you to convert your headboard and footboard to a larger or smaller size. You may also have a problem if your bed is constructed so that the headboard is permanently attached to the frame or footboard. In this case, if detaching it without damaging it is not possible, you may have to get a new headboard.