One reason some people like bamboo over metal is that it is less slippery and the stitches are less likely to fall off. But that has both advantages and disadvantages. Most knitters end up with a variety of different kinds of needles to use in different situations. The slipperiness of the yarn is taken into consideration in selecting needles for a given project. Some people don’t like grabby needles for anything (bamboo type), others like them for everything. Sharp points or not so sharp are also useful for different purposes.
Metal needles should be fine for your toy, if the yarn is very slippery and you foresee problems that way one of the coated types will probably be better. I also don’t think all bamboo needles are of the same quality and you may find bamboo needles that are small but don’t seem as prone to warp or break as others.