Lae'zel mentions she has faught lairs of beholders on the plane and gith warriors must bring the head of an illithid (she must hunt alone) to even be classed in the military caste. All this and you start as a new born baby. You kill a single beholder and you are level 6 from birth, same with illithids. Illithids are badarse CR 7-8 and beholders are absolutely crazy tough CR 13-14. A young red dragon what the gith dragon riders fly is CR-10. Killing one beholder is 11500xp. Bare in mind CR (challenge rating) is based off and entire group of adventurers.
Just saw this. Dunno what the rules are about double posting but I wanted to point out that Lae'zel admits she's never visited the Astral Realm before, which means she probably hasn't completed her rite of passage by slaying a mind flayer yet.
The PC can talk about the Githyanki city in dialogue so your PC can actually be older and more experienced than she is. It also shows if you let her interact with the Gith dragon-knight vs you doing it. Your character is a lot more well versed in Githyanki society than she is and won't insult the dragon-rider the way she accidentally does.
Lae'zel talks a big game but she's actually pretty young and inexperienced. I'd say she's probably the best of the companions for being a 1st level fighter. Fresh from her Creche and abducted by Ilithids and now terrified she'll die long before she can prove herself worthy.
Also, having killed cool monsters in your backstory is pretty common for DnD PCs. Especially as part of a larger group. Not everyone was a dirt farmer before they took up adventuring. And Hell, by your logic it should be impossible to make a level 1 Githyanki at all.