Hard to say. Construction factories on earth are going idle too. Also, there is a good roleplaying reason:
By shipping construction factories, the new colony can carry on if a war breaks out on earth. Making the colony self-sufficient is a pretty high priority.
Also, keeping the manned mines active on earth allows the Commonwealth to get the largest amount possible of the remaining Duranium. Keeping them active denies Duranium to the Commonwealth's competitors.
The alternative to shipping Construction factories to build infrastructure is to ship infrastructure directly. Granted, the Commonwealth could ship the infrastructure it already has. That just means that some number of people starve to death. But it is cheaper than building new infrastructure at home.
A bit of a political knot there.
Shipping construction factories may make it easier to conceal from spies what is going on at the colony. After all, construction factories could build anything.
How bulky is infrastructure? Is 100 Build Points of infrastructure harder to ship than 100 Build points of factories? That would be an excellent reason to ship factories.
All in all, colonies are likely to be much more industrialized than the home planet. I see several different types of colony:
1) Pure mining colony. All infrastructure and mining equipment are shipped. Perhaps planet has a high colonization cost, so is not an economical site for factories.
2) Supply base. A colony with large or highly accessible duranium might make a good advanced supply base. Has mines and supply factories and maybe a construction factory to, to keep up with population growth. Ship production you probably want to have fairly concentrated, but it could pay to have supply production dispersed. Plus, it has some nice roleplaying effects.
3) New Earth. Home planet is running out of resources, so rather than ship resources all the time to the home system, a new capital is set up. It will become the new site where resources are shipped to. Major production will be concentrated there, where it can be defended if necessary. Goal is to get the planet to the point where it can expand the total economy.
It is possible that a new warp point could be discovered back to the Solar system, or close to it. In which case there might be a massive shipment of colonists + infrastructure, but very little industry, as most of that would already have been shipped from Earth. In which case you would have a fourth type of colony, a sort of population holding tank.