Hello there!
Not sure if there are any mini dairy sheep out there, but there are mini sheep..and technically they all can be milked. The milk will taste the same, you just wont get as much if it isn't a "dairy breed". Look up "keyrrey-shee" mini sheep.
I have dairy sheep! (E. Friesian x Icelandic cross) I understand how hard they are to find! I looked and looked until I stumbled across a "dairy milk yahoo group" in my area. You might want to google one.
Pros about owning sheep:
They are dual purpose, you can use their wool, use them for meat and use their milk...unless you get a hair sheep (you can milk those too, look up katahdins, I also have one of those) then you can milk them and/or butcher them for meat.
Their milk has more total solids, fat and protein than the milk of goats and cows. (It takes a lot less of their milk to make cheese than a cow or a goat's milk.)
Sheep milk has over twice as much riboflavin B2 as cows and goats, double the Thiamine as cows and goats, more niacin B1, Pantothenic acid, B6, B12, and biotin than cows and goat's milk.
Even more calcium, phosphorous and magnesium than cow milk or goat's milk.
You can freeze sheep's milk for up to 6 months and it thaws perfectly, cow or goat's milk doesn't hold up well to freezing.
The milk makes wonderful soap and delicious cheese b/c of it's high fat content. Plus the milk tastes sweet and delightful w/o any strong "[goaty] essence" lingering.
They keep my yard perfectly manicured, and they don't need to climb on top of stuff like a goat.
The only down side to having dairy sheep (IMO) is that you can't make butter out of the milk b/c it is naturally homogenized.
You would be surprised how they are gaining in popularity these days. ("House cows" they are sometimes called.) The breeder I use says 12 years ago there were no dairy sheep in WA and now there are 5 large sheep dairys.
Hope this helps!
-Sally
disclaimer: I love goats too! Sheep just fit my lifestyle better.