How to reinvent measurement units? Imagine you're in deserted island. You will eventually need to know how much there is of something or how long is some thing.
Is there a way to get all main measurement units (kg, m, °C, m$^3$, etc.) somehow? I know water freezes at 0 and boils at 100. Also $G=9.8$ and $\pi=3.14159$. Also probably I could do something with pendulum, because I know $G$, but I wouldnt know time (from sunset to sunset 86400s?).
Are there some other valuable equations that could be used?
 A: Short answer: yes
Longer answer: yes, but it's hard
Assuming, that you somehow have accces to any information you want, you can get there but it's a long way that a single person can't do all alone. At least, if you want defined precision.
Get roughly one second: let something dense fall from 4.9m (but for this we need to know how long ma meter is).
Precisely get one second: get a lab full of gear to measure the frequency of the  hyperfine transition frequency of the caesium 133 atom. 9 192 631 770 of those transitions is one second. But doing that is quite hard in a Lab (Curious Marc mad a wonderful Video explaining the Process) and even harder on an island.
1 metre: About the length of a long step...
A bit more precise (as already mentioned in the comments): 1/10000000 of a meridian from aequator to pole (depending on the size of your island not as easy to do)
Precise: get a Lab full of equipment to measure how far light travels in 1/299792458 of a second...
So creating any measurment unit is basically just like saying "I declare this, being a unit of that". Recreating the SI units is a huge task that took an army of scientists decades if not centuries to get to the stat we have today (and they are still looking for better ways).
So yes, recreating the SI units is possible but not alone on a remote island.
