When I was fit and in training, I used to ride for an hour non stop and then check the distance covered. On a Coker with 150s, my best was 12.95 miles in an hour.
I also once did 22.5 miles in 2:15 on the 700c x 23mm with (from memory) 114mm cranks. 10 mph average.
Now I can’t even hit that speed briefly.
To have the best chance of keeping up with a bicycle in general, you will want the fastest unicycle you can afford.
However, this really depends on your wife and, to a lesser extent, on you. My wife rides at a very leisurely pace, and it’s no problem riding alongside on my ungeared 29.
Do you know the pace you’re hoping to match? How much extra work are you willing to do to match it?
You got that right.
I’ve started using a gps tracker for my rides. Quite amusing much as I think this raises my geek scale another notch. 
Yesterday’s ride was downtown dealing with pedestrians, stoplights, crosswalks etc.
On a 24" muni 2.5 inch wheel: 7.2 kph (4.4 mph) over 5.55 km (3.44 miles). Includes the accumulation of 7.5 kg (15 lbs) of groceries.
Definitely not as dangerous as the Colbert Report suggests. 
I’ll be curious to track some rides where it’s more of a ride as opposed to a grocery run.
Edit: Just getting into the program details. Apparently I can cruise at 11 kph (6.8 kph) for a sustained period. Stoplights really mess up the data. 
I normaly ride at 17/20km/h on my ungeared Coker with 114mm cranks. I’m trying to get faster sometimes. I did a 30km ride once without going under 20km/h, I did the ride without any stops. I’m going to take my Coker out again since all the snow melted and I’ll be looking for some other long and fast rides soon
I have a geared 36, and when I go out for rides, my cycle computer generally shows an average of 17-20km/hr, depending on the hilliness and how spry I’m feeling that day.
On my ungeared 36, I would have mostly similar averages, especially uphill, though with the gear I am more likely to have a 20km+ average speed - without the gear I am more in the 16-19km/hr range.
If you look at my top speeds however, on an ungeared I could barely beat out 30km/hr for more than a few seconds, while on the geared I’ve topped 40, and holding at 28-33ish km/hr is actually quite comfortable when conditions are favourable. I find that for me, the gear allows me to use my energy more efficiently, and to go faster for longer. In the long run if I’m not racing though, my pace tends to stay mostly the same, but I’ll have more energy at the end of a long ride. Fast cadences on short cranks are waaay less fun than pedalling slower and going faster!
My 36er is an ungeared kh, and My “comfortable” average speed has gone up from about 11mph, to nearly 13mph, since my uni century on 7/11/10. I think it’s because I’m spinning more efficiently, and wheel “wobble” has pretty much been eliminated through smoother technique.
Plus, since I added my aerobars, it’s really helped keep me “loose” and relaxed, which also helps me to spin more efficiently. I’m still using 110mm moments exclusively, and may try going to 102’s just to feel the difference.
Using my new 36er (first one) I was averaging 10-11 mph yesterday at cruising speed.