No Such Thing as the Plank Length?

I've been tossing this one in my head for a while now, and every time I think of it I convince myself that there is no such thing as the Plank Length (i.e. smallest unit of measurement) because of this following situation:

We have two observers, we will consider one of these frames of reference to be stationary and the other travelling at half the speed of light. From the stationary frame of reference, the observer measures the plank length to be 1.616×10^-35 m. Lets assume the stationary observer is very clever and can accuratly measure a plankian distance on the second frame of reference travelling at a sizeable portion of the speed of light. He would measure the plankian length to be 1.399×10^-35 m, a small but noticably smaller length than his. He continues to measure, and each time the speed of the second frame of reference increases until at 0.999999c, the measured plank length is 2.285×10^-38 m. Now all that has to happen for a smaller distance to be measured is for the second frame of reference to bump up its speed a little (disregarding the huge amount of energy needed to do so). Therefore, the plank length can be as small as we like, so whats the point? I know that the plank length is not measured but calculated, but supposing it could be measured, would this not happen? Do we make the plank length immune to length contraction?

It would be great to discuss this

 

Ok yes, if the Planck length is where general relativity and quantum mechanics are supposed to be unified, wouldn't this mean at relativistic speeds it would appear to be unified at a much smaller scale - and following from that, if the speed is great enough, wouldn't there be no need to have a unification? (since the Planck length is infentesibly small)