Also, Prague station as well as airport bus has pickpocket(bus)/purse snatching(station) nuisance.

If living/visiting Prague and wishing to go to Vienna city, I would not bother with air (bus or train is easier)
But when arriving at PRG, connecting VIE by air make sense.
T1 and T2 are connected

However, you are making international to "domestic" connection at PRG, so you will do your schegen entry at PRG (allocate few minutes for that process)

If your plane is on time, this connection is doable.
Otherwise you could be SoL as there are two separate tickets involved.
As a matter of policy, unless second ticket is flexible, I avoid close connections on separate PNR (in fact try to avoid separate PNR wherever possible)



City transport (avoid CAT, just take regional S7 for 4.40 Euro) is easier/safer at VIE.