Do the experts here think the overall land speed of the unicorn will match or at least come close to that of the dodo?
Well, while it appears the Dodo was fairly swift. Using a modern proxy, the ostrich (as a large, land bird) runs about 40 mph, I'd put an uneducated, non-scientific guess at about 25-35 mph peak speed.
Assuming that the origination of the Unicorn is from people seeing Rhino's, the White Rhino can run about 31 mph at peak.
If, instead, the Unicorn is really someone's great practical joke and it was simply a horse dressed up, a Quarter horse can run about 47.5 mph.
So, if a Dodo and a Unicorn made a bet as to who would get the land-speed record, if it's a Unicorn based on a White Rhino, it might be a toss-up. If it's a Unicorn based on a dressed up horse, pretty much the horse would win.
And now I feel all proud and geeky and self satisfied that I have go through the time and effort to attempt to make an absolutely meaningless point about something completely unrelated to the original topic.