Let's start with some basic propositions. Australian residents must pay Australian income tax on any and all income that is not otherwise exempt: s 6-5(2) of the Income Tax Assessment Act 1997 (ITAA97). That includes money derived from foreign sources. Non--Australians must pay income derived from Australian sources: s 6-5(3) (see http://www.austlii.edu.au/au/legis/cth/consol_act/itaa1997240/s6.5.html). You are also required to include in your Australian assessable income any amount that is considered to be statutory income: s 6-10. We'll come back to the concept of statutory income shortly.

The definition in s 6 means it is important to determine whether you are an Australian resident for the purposes of ITAA97. The definition of the expression in s 995-1 of ITAA97 unhelpfully says, in effect, you will be a resident for the purposes of ITAA97 if you would have been a resident for the purposes of the Income Tax Assessment Act 1936 (ITAA36). That section suggests a resident is:

"(a) a person, other than a company, who resides in Australia and includes a person:
(i) whose domicile is in Australia, unless the Commissioner is satisfied that his permanent place of abode is outside Australia; [or]

(ii) who has actually been in Australia, continuously or intermittently, during more than oneā€‘half of the year of income, unless the Commissioner is satisfied that his usual place of abode is outside Australia and that he does not intend to take up residence in Australia;..."

I'm assuming (ii) doesn't apply to you, so we are left to ask: Do you reside in Austalia? That is a question of fact, and the term "reside" is given its ordinary meaning. To determine whether you are a resident, the Comissioner would typically take into account factors like:

your usual place of abode (in your case, Doha);
the location of your family (if any, including wife, children, parents etc);
where you keep your personal effects (with you in Doha, I imagine);
the purpose, frequency and duration of visits;
your nationality and citizenship (presumably Australian); and
any social ties you have with Australia.

You may still be considered to be domiciled in Australia if you were born there. Arguably, you have elected a new jurisdiction to serve as your permanent home or place of abode, ie Qatar. The factors relevant to determining your place of abode are listed in income tax ruling IT 2650, which is available online. (It also includes a discussion of the other part of the definition in s 6 that was covered in TR-98/17.)

If you are sending money back to Australia, the ATO will find out about it. If it is being held in an Australian bank account, for example, it will accrue interest that will be considered to be assessable income.

Is that a start?