Indeed, you are correct, the New Covenant did away with the need for the old levitical priesthood as all born-again believers are priests, whether male or female.
Speaking to Christians in general, the apostle Peter wrote:
“You also, as living stones, are being built up a spiritual house, a holy priesthood, to offer up spiritual sacrifices acceptable to God through Jesus Christ. ... “
“But you are a chosen generation, a royal priesthood, a holy nation, His own special people, that you may proclaim the praises of Him who called you out of darkness into His marvelous light.” I Peter 2:6, 9