She is really strong. Her W (rank 5) is 210 base damage with a 1.4 AD ratio with a 1450 range. 6 second cooldown, and it's a 70% slow, meaning 70% slow every six seconds. Sure, it's a skillshot and it only hits the enemy it collides with, but combine that with armor pen (Last Whisper) and some heavy AD (Bloodthirster), you can get some good damage. I had 340 or so AD and the extra damage on W was +440.
Her Q is also really strong. Like you said, 700 range at rank 5, 3 units less than Tristana at level 18; at level 9. The 130% attack speed on the 3rd hit is also really good- so far, it seems like every shot from her rocket launcher state takes 20 mana, and that's 700 range + the AoE damage can critically hit.
Honestly, I don't expect people to use her rocket launcher state as much as her minigun, but for long range chases, maybe. I have called her overpowered multiple times while playing her, mainly because she's super strong, and has the most CC of any ADC that I can think of. Also, her snare is 1.5 seconds (as mentioned) and has 340 base damage.
Her ult (at rank 3) is also 250 minimum damage, and 500 maximum damage + 35% of the enemy's missing health, and does 80% damage to nearby enemies as well.
She'll be godlike at chasing, with the 70% slow every six seconds, on top of champion kills and turret kills giving her 175% movespeed.
She's ridiculous.
Definitely expect some nerfs coming to her numbers.