Ironically, the Disney Visa is one of the least valuable cards for a Disney vacation. Sometimes they have a nice sign-up bonus on offer, but otherwise, 1% in Disney Dollars for every dollar spent is going to yield pocket change.
For Southwest, I agree with the above poster who recommended the Sapphire Preferred. You'll get 50,000 points instead of 40,000, and you can transfer whatever portion of those you want to Southwest to cover flights and keep the rest in the Ultimate Rewards program to be used however you want.
Since you only have one card and are allowed up to 5 before Chase would cut you off, I'd recommend going for the "trifecta" of Chase's Freedom, Freedom Unlimited, and Sapphire Preferred (or Reserve if you can justify the higher annual fee). I'd get the Sapphire first, use it exclusively to hit the sign-up bonus (you have 3 months). Once that bonus is achieved, apply for one of the other two. Use it exclusively to hit the sign-up bonus. Then complete the trifecta with the last card, use it exclusively to hit the sign-up bonus.
You'll wind up with over 80,000 Ultimate Reward points, which are transferable to Southwest at a 1:1 ratio. You'll also have a point-earning system for the long haul: Chase Freedom for 5X rotating quarterly categories, Sapphire for 2X or 3X on dining and travel, and Freedom Unlimited for 1.5X on everything else. You're allowed to combine all points on your Sapphire card, where they can be transferred to Southwest or many other travel partners (airlines and hotels), or you can use them through Chase's travel portal (no Disney resorts though...as I just found out), or just redeem for straight cash back.
Sorry for the long-winded reply. The short answer: You're fine to get a new Southwest card. You can get more than that if you want too.