Tarin,
First, welcome to the Flute board. You will find that there is lots of helpful information here, and that your question has been asked quite a few times before. You might want to take a stab at looking thru the archives using the search function.
There are a couple of related side issues that should contribute to your decision. When I was in your shoes, they primarily resolved into intent, proficiency and economics. In other words, what are you trying to accomplish with switching to the “tenor” octave (playing in sessions, church, for yourself…)? This will help you decide whether you need a Low D instrument that is in A440 with a tuning slide, or can get by with a, typically less expensive and often easier to play Eb or F flute, one in a non-standard tuning, or low G whistle. For proficiency, where are you now with the whistle, and how far back are you willing to go to work out a flute embochure? If you have progressed past the beginner stage on the whistle, you will most likely find the Low D whistle easier to pick up and play. Of course the economics is obvious. With unlimited funds I would advise getting the best quality instrument of each type you could afford, and trying them out to see which you prefer. As you are probably aware, there is an active market, here and elsewhere, for good quality instruments, so whichever you decide you don’t want, you will be able to resell.
However, the likelyhood is that you are asking the question because you are not in the position to buy whatever suits your fancy. Flute and low whistle have similar, but significantly different sounds. You can check on YouTube, or on many of our member’s posts for good examples. If you have a strong preference there, your decision is easier.
My personal recommendation would be to get your hands on a decent relatively inexpensive, simple system flute (Tipple, Murphy, Hamilton student, Burns Folk) and practice with it for a while to see if you can work out the embochure issue. For some it is easy, and others a struggle they are not willing to take on. Personally I have had a hard time developing my embochure, but now at almost two years into playing I much prefer the flute and chose it preferentially over my low whistle. I find that the transverse fingering of a conical simple system flute (particularly a smaller hole Rudall style) a lot less stressful than a cylindrical low whistle, and I have rather large hands, but each to his own.
Best of luck with your decision in any case, and nice work with the english in your post.