If all of your users are on AOL, using the AOL dns servers and you have a long TTL, then you will need very few queries.
But, with failover your TTL has to be short to be effective.
Then, there is the matter of time scheduling. When do the bulk of your users arrive at the site.
There are sites in my experience that use upwards of a couple of million queries per day on a TTL of 24 hours. Problem is they don't disclose their web traffic. So, no correlation can be made.
Email is also a heavy consumer of dns queries due to the way some spam control systems work.
For web traffic only, you would seem to be in the quarter of a million per day range. Give or take. But the margin of error is quite high.
Can you separate out the bandwidth consumed by your dns currently? That could give you a good idea. Estimate on outbound, 100 bytes per query would put you in the correct ballpark for that particular TTL. If you change the TTL, it will have an almost straightline relationship.