All of the points that Bill raised, plus..
1. Don't underestimate the difficulty of getting an approval from your local health inspector. In some jurisdictions this is relatively simple, in others it is all but impossible to get an approval for a homebuilt oven. Some have even had to pay for UL field certifications to get over this hurdle. Not to mention that some inspectors will insist on 5-compartment sinks, potable water, refrigeration & a host of other things. Call your health department & find out where they stand on all of this.
2. A masonry oven is going to be a lot less robust than a terra cotta type precast sectional oven. So a masonry oven should be very well built to stand the rigors of transport, potholes & so forth. Definitely make sure that your trailer has some kind of suspension. Unfortunately, I don't have more than anecdotal reports of mobile masonry oven having problems so it's hard to say exactly where the line on this is. While there is no doubt that the precast ovens are structurally stronger, a well built brick oven should be fine. But I would err on the side of having it overbuilt for mobile use.