Am I ready to solo Horntail?

I don't know if you would be able to kill it if it takes you 30 minutes to kill Zakum...
You won't be able to kill it if it takes you 30 minutes to kill Zakum. The two preheads alone have far more HP than Zakum does.
I would get a partner (a Phantom or Bishop if possible so they can protect/revive you if necessary) so you can get the hang of things and then try a solo later on.