If DQ is included in your ticket and you have a wet afternoon free, I'd say go for it. If, however, you'd have to pay extra to get in, or it would mean missing something else that you want to do, I'd suggest you give it a miss.
I always quite enjoy DQ, but as we always have a reasonably long stay in the World when we go, and as it's always included in our tickets anyway (the UK Ultimate tickets), it doesn't 'put us out' too much. There are classic arcade computer games, air hockey tables and some good interactive games, but it's not worth missing a day at MK for.
If you do go, the Pirates game is a good one, and you should be able to take your dog onto that without problems.
I'm afraid I can't remember, do you use a chair, or not? If you do, I ought to warn you that some of the classic arcade games were not exactly built for those at our height. Also, I've had to develop a completely different throwing technique for skee-ball (think air hockey movements and you've got the idea). Also, for any chair users out there, be aware that they really didn't think when they chose the flooring - half the time it's thick carpets, which are a beast to push through and pull you off in different directions.
All in all, fairly nice distraction for a rainy day, but not worth a whole pile of extra money or missing out on other Disney stuff in my opinion.
Well, that was a long and rambling post! Have a wonderful trip, whether or not you do DQ!
P.S. If you do have unlimited free entry, and are close by (e.g. PO, OKW or SSR), you can get free internet access in the Wonderland Cafe (WARNING: not well designed for wheelchair users).