Firstly, as I understand it you will only be able to apply for non-resident status (i.e. tax exemption) if you are going to be out of the UK for a complete tax year - i.e. 06th April -> 05th April (approximately). If you're only coming out here on a 1 year contract and you will be in the UK either side of that year then you will probably have to pay UK tax on your earnings made in Qatar.

I believe P85 is the correct form to apply for non-residents status (the form was called 'Leaving the UK' I think). Once they've received this they will ask for some more stuff from you (P60, P11d etc - stuff from your previous employer).

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