Phenol is benzene with an extra oxygen tucked in to make it hydroxy-benzene. Phenol is a basic building block of many, many organic molecules and is not inherently bad, it depends on what else is in the molecule and what it might react with. If it has an extra carboxylic acid group in the molecule, you have
salicylic acid, the compound in willow bark that aspirin is made from.
Phenol is not generally found in nature since it is quite reactive; it was first extracted by distillation from coal tar, and can be made commercially by a variety of routes from fossil fuels. It is used in all manner of chemical processes, from plastics to pharmaceuticals to antiseptics. Good ol' Campho-Phenique is
camphor and phenol in a mineral oil carrier and has been used on cuts, scrapes, and bug-bites since 1884.
Your concern with the compounds emitted by wood chips has less to do with phenol per se and more to do with the sap, tar, or resin that is contained in the wood. Many of the compounds in plant-based goos are in the class of chemical compounds called
terpenes, and while a little bit of terpene, like the essential oil from hops or lemons, can impart a nice flavor to your favorite beverage, a swig of turpentine (pine tar terpenes) can be toxic.
Since alders are in the same family as birches and hazelnuts (
Betulaceae), the sap is more likely to be able to be made into a beverage (birch beer) than to be distilled into turpentine, and so it is probably safe for your chickens and rabbits. Of course, any animal can have an allergic reaction to almost any natural product chemical under the sun, so you would want to add it in little by little to the bedding or litter and watch for any adverse reactions.