Space ship is the suit.
If it wish to get some information about tiny speck of dirt aka planet it uses proper tool for that, like probes, cyborg ants
As multicellar organisms astronauts do not disassemble them self to visit space—main reason they could not enjoy that visit in same way as they do it now, mostly because of disrupting consciousness.
Although being organism of organisms may have some advantages.
Incorporate some implants maybe easier in form of devices, sensors, tools—because we as example are pretty dense packed organism and are not very stretchy, kinda of. Close connection, with is very important for proper function on cellular level, between cells, makes it not so easy to embed something in between.
Anthills need lot of tools to build ships for they sizes, lot of advances. So even long before they go in to space, they might have to develop abilities to incorporate tools in their "body", at least manipulation tools, tools they have to use to affect and extend effects and project they will on surrounding environment, extend their capabilities. It might be obligatory just to develop and build everything they might need for such transition.
Actually it's a heaven for those who dreams about implants, cyber-parts of their body etc etc to extending their own capabilities. For anthill it's a reality, long before space. He might get so much advantages from it. His fear will be not about inventing super intelligent AI, but replacing himself completely with that AI. He is well suited for that transformation, from our(in this case my opinion, but depend on AH internal construction) point of view.
Making suit for single ant is actually possible—with communications etc.—but that highly depends on anthill internal organisation, and may be not so brilliant idea but technically possible. With cells as ours—making suits for them, hm maybe kinda possible, not sure, but it's more difficult because cells are quite small by themselves, but main problem interaction between those cells is on molecular level, between molecules and clusters of such molecules, and molecules are from atoms, which we may actually count—and here starts problem with cell suit, in case if we have to make it from another atoms, because of quantum mechanics and because of properties they do have which they do not have when they are in big quantities of atoms. (more I think, more it seems unlikely for cells suit idea—very hard task)
But for anthill cells it's different—until their interaction is on level where interaction is done by relatively big number of atoms as of groups of cells (instead of molecules and clusters of molecules in our case).
Also nice thing about implants and tools—their stone technology would be our microtechnology and next level is nanotech. Anthill's will start from micro instead of stone axes of our ancestors. They will extend their stonetechnologies in macro level direction (which we have started from) and in nano direction.
We need lot of stuff to manipulate objects on micron level, we have spend at few centuries of technological development to achieve that results and build microprocessor, and it took us significant amount of time from stoneaxe time to get here. And they will have hundreds and maybe millions years to perfect their "micron out of the box" abilities
Space ship itself may be very much different, from what you may think as space ship, specially looking at concepts depicted in literature or projectrho
V2 rocket path is not for anthill. Microbots swarms, tethers and so on, this way it might go. It might have to lift not only its own substantially big mass but also it skull-shell—where this mass works properly. But as skull is not part of his body—it's ok for anthill to make one which is capable to leave planet(at least next generation anthill). So space ship is even not a space suite, but space skull for that anthill. And it might be able leave planets and land on planets.
It might be multipurpose tool for that anthill. And space ship which hosts such spaceskulls, if it is the case which is not necessary true, might be just bigger tool with connects their personal tools (or they form this bigger tool by connecting their personal tools).