You really do need a load calculation and load test to see if 125 amp panel is enough to add a 50 amp breaker.
The double breakers count as a 240 V load, the single breakers count 50% as they should be some what balanced.
Right now your absolute max load is 180amps at 240V.
Your 125 amp service breaker, should be 80% de-rated, or a max continuous load of 100 amps.
Each of your "large" loads, such as AC and Dryer should only draw a max of 80%, but could peak above that for short periods of time (like when the AC first kicks on).
Once you get your overall load situation looked at, if it is still too high to comfortably add a 14-50 (with a 40amp draw), you may want to consider putting in a 14-30, which would have a 24amp draw, and would still charge a Model 3 at about 20 miles/hr (would charge a Model X at around 15-17 miles/hr). If you install a 14-30, put in a 30amp breaker, and the 14-30 outlet, but size the wire for 60 amps in case you upgrade the panel later, and want to put in a HPWC, or a 14-50 outlet. A 60 amp CB with the HPWC lets you charge a model S or X at 48 amps (and I presume model 3). The cost of the copper wire will be more expensive, but not as expensive as running it again if you upgrade.
The cost of a panel replacement may best be done when installing Solar, as your panel is not large enough, nor the right configuration for Solar, and the panel upgrade would probably count as part of the installation cost of the solar for tax incentives.
-Harry