Agreed here. The EQP/BQP solo adventures are very difficult as written, and are likely to turn away a noob HQ player with a basic character once they get killed. So upgrade your hero first.
I tried playing EQP 1 with a basic Elf and a basic Barbarian. I gave them each a 2 BP mercenary (random draw) and I also gave them each a random Equipment draw (they each ended up with a piece of armor). It went very well and was a lot of fun. This compared with an equipped Elf (6 defend dice, 3 attack) who gave up after her character was reduced to 1 BP in a stalemate with a mummy. If I had forced the player to pick Earth spells it would have been a lot easier (she picked Fire), though.
BQP 1 & 2 were okay for an equipped Barbarian (4 defend, 4 attack, Armband of Healing) but he died on the third one, so I brought him back with some low level mercs (4 with 1 BP each). Without tweaks and with a basic hero, I'd say they are very unfair and so adding your own stuff, even another player, isn't "wrong" by any means. In an ideal world they would have play-tested them and balanced them for a basic beginner Hero. If you want those types of quests, check out the early adventures in the Japanese game system.
I still love the IDEA of a basic solo quest, so I'd say either being more generous with the treasure weapons & potions and having more manageable monsters (fewer and/or weaker), more forgiving traps, are all ways to ease a player into things without making it boring. Build up their confidence before you destroy them in the really hard quests later...

GS-->KK-->ROTWL--->EQP--->BQP (and somewhere in between there, AtOH and WOM, and either the Dark Company there or maybe at the very end!) but you play them in the order you wish. I think they grow in complexity based on release order, so that is a bit of a natural guideline (though EQP/BQP were intended for the NA audience and AtOH/WOM intended for the EU). Carrying your character from one to the other is more fun usually and I think they specifically wanted you to keep them from base game into the first two expansions at the very least. The EQP/BQP intended for the other heroes outside the solo quests to already be equipped, so you would have played something earlier. The books for the expansions even recommend if you haven't to at least play some of the GS quests before attempting them, mostly for familiarity. But you can also do the random equipment thing to make up for the lack of gear.