The ARRL welcome pamphlet contains instructions on building a simple ground plane antenna and specifically comments on its use by handy-talkies. However, I wonder what the actual capability of this antenna would be. Could it handle 25 watts? 100 watts? Does anyone know?
Without seeing the design you are referencing it is difficult to provide specific answer.
In general however, the most basic VHF antenna designs will work with a 100 watt transmitter. There are some considerations as the power level rises:
Higher power transmitters are generally more sensitive to SWR problems. This may cause them to cut back power, overheat, or in a worst case, fail. You may need to tweak the SWR more carefully for these power levels.
As the power increases, the voltage along the antenna increases. This could result in RF burns or arcing. Care should be taken to avoid injury or damage.
Higher power transmitters pass more current through the antenna. This can result in inefficiencies from, and heating of, small gauge wires and similar connections.
As power is increased, your RF exposure increases. You should perform an RF exposure assessment for the location and power level of the antenna involved to ensure that you are within safe limits of exposure.