I *ASS*U*ME* you have done enough research and are modulating the IR with a carrier frequency compatible with the Panasonic TV's IR receiver module.
You are using crappy LEDs without proper datasheets. The ZD1945 product page claims it has a max pulse If rating of 1.2A, but that isn't a whole lot of help if you don't know the pulse duration or the duty cycle. One could *ASS*U*ME* that the duty cycle is simply 50mA/1.2A, or fractionally over 4% but as Joule heating is proportional to I
2R, we already know that the simple ratio isn't trustworthy with such a large difference between the peak and continuous currents. Jaycar are very much the bottom-feeders of the retail component business, and the actual specs of their IR LEDs probably vary depending on which manufacturer's rejects they are buying cheap this month.
For comparison, take a look at the data available of a named brand IR LED from a reputable distributor, e.g. Vishay
TSAL6200. Not only is it rated for double the continuous current, but they provide the manufacturer's datasheet which includes graphs for radiant (optical) power vs current, and pulse current vs duration for various duty cycles. That gives you the data you need to push it hard without burning it out.
To get good performance you need to drive the switching transistor HARD to make sure its fully saturated. Typically one would use a forced Beta of 10. i.e. Ic/Ib=10, to provide sufficient excess base drive to minimise the Vce_sat drop. However an Arduino can only provide an abs. max of 40mA drive and you run into problems with voltage drop when you go much over 20mA, so you'll probably have problems pulsing the LED with more than a couple of hundred mA. Frankly, it would make more sense to use a small MOSFET, - something good for a couple of Amps, with a gate threshold voltage under 2V, low Rds_on, and low enough gate charge and gate-drain capacitance that you can meet your desired switching time requirements with only 25mA gate drive.