JerryH....I've never ever seen a combined dab radio/cd player much less one capable of wireless transmission. However, I believe there is a solution which might help but both will involve having to load cds into your computer.
You should 'rip' all your cds as WMA 'Lossless' to ensure the maximum sound quality in terms of future output. Your soundcard should have a speaker output. If it does, I would recommend a pair of FM headphones. The base unit acts as the transmitter and the headset acts as the receiver and, usually, has reasonably good reception over a large area. My own soundcard is an Asus Xonar D2X linked via the speaker output to a Sennheiser HDR 130 base unit which is then fed into the headset.
The alternative is to buy an internet wi-fi radio which could be linked to the computer to play sound files on your computer. That way a wireless router could be configured to link with an internet radio which can then be carried room-to-room as you suggest. You will still have to 'rip' the cds onto the computer for even this to work.
I would then suggest you 'rip' the cds to the free WinAmp and import all your cd files into this. (I have no liking for Windows Media Player sorry.) By creating your own playlists, you can feed it into either an FM headset with base unit, or run the feed into a wi-fi internet radio which supports WMA. If you feel ambitious you could add a small plug-in which would automatically mix the tracks and play them radio style. In either case, both will allow you the freedom to roam around your home and still listen to your music.
I hope my solution allbeit long-winded might help!
Big L 266