The Literal Commandment
You shall speak to the sons of Israel, saying, 'This shall be a holy anointing oil to Me throughout your generations. (Exodus 30:31)
Earlier in chapter 30, G-d commands a specific mixture of spices to be created for anointing the tent of meeting, the ark of the testimony, and the other furniture and utensils of the tabernacle. This verse indicates the commandment is an ongoing and perpetual commandment.
While Scripture says the creation of the oil shall be "the work of a perfumer" (Exodus 30:25) it does not specify a male or female perfumer nor does it specify that a Levitical priest should create it.