How low carb should a type 1 go?

You will need to adjust insulin dosing to compensate for the reduced carbs.
With very low carbs you will need to adjust insulin dosing for protein.

Assuming you are on basal/bolus rather than a mixed insulin, provided you adjust insulin to suit you can lower the carbs to any level.

Take care if you go very low carb.

I found bolus dosing a huuuuuuge challenge and gave up. For me, when I ate less than 20g carbs for a meal, I needed to bolus for protein and that it when the challenges started.
Protein timing differs and protein doses differ. I don't eat meat but found the timing and insulin to protein ratio was different for every type of protein from cheese to eggs to nuts to salmon to prawns to ...
My BG was up and down like the proverbial. And hypos can only be treated with carbs which means low carb was constantly going out the window.

If you can master this (or if your body is not as awkward as mine), you should be able to eat as anyone without diabetes whether that is vegetarian, vegan, low carb, high carb, low fat, high fat, ...
Personally, I would not use very low carb for weight loss. But your body may be more accommodating