IF you're on time should not be a problem. I've done less than 30 minute connections between terminals there walking at a brisk pace.
If you're on the partner that flies regional jets you'll likely come into terminal B and likely be leaving out of C or E. C and E are connected but you'll have to take a train from B to either. Pretty efficient operation, hike to the train, go up a level, get on, get off, go down, hike to gate.
If you're on the partner that flies the prop planes you'll likely go into terminal A where shuttle bus is the connection mode and I've had mixed experiences. The bad is - land, wait for shuttle, go to terminal A, wait for shuttle to C/E at a gate with staff who have absolutely no sense of urgency whatsover, take shuttle to C. The good is - land, not 1 but 2 shuttles show up, 1 to A, 1 to B/C/E thus eliminating a transfer, informative, energetic driver so go figure. Hopefully, the good experience becomes the norm.
What I'd suggest, since you don't have a lot of slack, is check the departure from Houston of the flight to Corpus that turns around to be your outbound to Houston. If there is a significant delay and its not a ground stop in Houston start investigating alternatives..that will give you an hour or so lead on everyone else who won't know its delayed until they post it.
