Sikh: No problems as long as you dont carry weapons (kirpan) or chant in public (kirtan). That said, whatever you do within your own private home does not concern the authorities (as long as you are not being a 'social nuisance' and some one complains about you).
Veg: Lots and lots of options ... there are many vegetarians here in Qatar who will vouch for a whole range of hotels that are pure veg.
Qatar is a very tolerant Islamic society so dont be worried about being singled out for being Sikh. As long as you obey the law, you are doing OK.