I ran into the same issues with Summoner when I was levelling it too, especially when it came to certain job quests that you have to do solo.

I found I could just squeak through the fights with a couple of 'tricks'...

1) Chocobo. Gotta have your Chocobo out for a little extra damage and the occasional heals.
2) Healing potions. It's not much, but surviving by the skin of your teeth is still surviving.
3) Gear. Most importantly your weapon, but having gear that is 5 or more levels below you is an anchor that drags you down.
4) Keep moving. Spells that are instant cast are going to be all you use. Run around in a big circle so that the enemy mobs can't hit you. Stop and cast a big spell or a heal when the enemy stops to use a long cast of their own.

These got me through to 80, and I was not a Summoner main at all so I had almost no idea what I was doing.

Hope it helps you too.