I support idea, anything that makes firemaking more interesting skill than rather just tedious process of burning logs at casual spots(like G.E. or elsewhere).
Now, for feedback:
Mind explaining in details, how you picture it would fit in our server?
Surely, you have thought about it that adding newly baked area will take time and mechanics to be implemented too? Otherwise, I strongly suggest explaining it in more detailed way. From what I see right now, there is nothing but plain rewards listed in both paragraphs with any slightest mention of how they will fit our server.
Pheonix pet - good, model can be taken from the ones that GWD birds use and recolored with fire color + made flying like those of Donator Dragon pets.
Book of Fire, or should I say, Tome of Fire(+burning pages) - I can see it being used in areas like Vyrewatches or Ice Strykewyrms(monsters that are weak against fire spells), other than that, it was designed mainly for pure pking, as it enchants fire spells without the need of defence levels.
Pyromancer Suit(I did some research since I played long time ago OSRS) - should either be equivalent(or better) to what Golden Mining set is to Mining/Smithing skills in terms of bonus effects, otherwise there is plenty of cosmetic to have ing, I suppose do some clues to see for yourself about that.
I kinda missed one thing from this list out. What about Dragon Axe obtained by skillers? Why it is not mentioned on first row in listed reward table since originally this minigame is build to be for both Low-level and High-level content? Could be less common than from monster killing, for example, 1/250 or 1/500, highly depends how long will it take to get boxes.
Assuming this makes it to updates patches next year probably, I love the concept of this suggestion but try to be more detailed and be prepared to explain what everything stands for even though at the end of the day, you still have "Yes" from me.