I believe you should study A+ and write the Certification when you know you are ready. This is a basic certification and on its own will open doors for you. I too have A+.
As far as Networking is concerned, I am an MCSE Windows NT 4 and I learned lots about Networking. I didn't know anything about Networking before I became an MCSE. Since becoming an MCSE I continue to learn lots more at work and also by building a Network at home too.
That is only one level of Networking though. I have since learned about Routers. I am presently involved in self study about CCNA, Cisco Certified Network Associate. This is a beginning certification leading toward CCIE, Cisco Certified Internetwork Engineer.
I have foung that Both levels of Networking are necessary to get the hole picture. I am also Certified in A+, but I am not familiar with Network+ except to say that I understand it is pretty much the same as Microsoft Network Essentials which is part of getting ones MCSE. The point is that if you decide to become an MCSE you will be studing Network Essentials anyway and therefore Network+ is redundant.
Consider MCSE and CCIE as two sepatate levels of Networking. One level ( MCSE ) mostly considers what goes on in an Organization, ie: USM and the other level of Networking ( CCIE ) is about how you network using WAN Technology to go from site to site or different locations geographically within an organization. These are two separate paths in Networking although there is an ovwerlap.