Hi gbob and welcome to the forums
If you still have Tucson -- the Off-Map-Box second from the bottom on the far left edge -- Dallas will draw supplies through that as long as your need are rather modest and deep winter hasn't set in. With the cavalry regiments you get, at first that should be no problem.
Your problems will begin with trying to hold on to Dallas with just those cav. regiments; I thought it was 3 actually. IIRC the event also gives the CS a small force down in Houston with some infantry and a battery of artillery. Without reinforcements your cavalry will not prevail against this force. And here is where your problems start. Missouri will already be at least a minor -- at least -- conflict and it is very difficult to spare any troops to reinforce Dallas, plus the distance is very extreme even if you can spare any.
You have an artillery battery on the West Coast, plus some cavalry and infantry, which are of little use out there; plus they are first rate regular army troops. As soon as they are free to move I always send them to Denver and then depending on the situation portion them out to Tucson, Kansas, Missouri and the Indian Territory. It's a long march getting to Denver and I always set all the moving troops to Passive Posture to retain as much cohesion as possible; there is no chance of them being attacked on their way to Denver at this stage of the war.
You should also consider sending a leader to Dallas to bolster your defenses. Even a poor 3-1-1 leader will improve your defenses even when he is deactivated, which he will be half of the time. Just don't count on him too much on the offensive.
The only other way to bolster Dallas' defenses is by creating a diversion by invading Texas along the Gulf Coast. It doesn't take that long to send troops from the East Coast down to Texas by transports, but from where to take them while you are trying to build up your armies east and west already. The invasion strategy also had the disadvantage of leaving you with 2 separate forces which cannot support each other directly and the South could hit one force and push it out and then take on the other with only one battle group as they have the inside track and the ability to decide where to fight first.
All in all it's a very difficult conundrum and in the hand-full of times I've run into it I only once came close to holding Dallas by reinforcing through Tuscon. I ran into bad luck with weather which blocked supplies and with weakened troops I got pushed out of Dallas and barely got their remnants away without being destroyed.
Before you let what ever forces you have in Dallas be destroyed, I'd abandon it and hold onto Tucson and Laredo. Better to take what you can get than lose it all.
Good luck.