Its impossible to tell, as there are no definitive guidelines, but I would seriously doubt it. This is a dispute over pay and conditions. Just because you are unhappy about the pay and conditions does not usually make it reasonable to give up your job. Also, travel expenses are not necessarily designed to pay for your entire tax and insurance, only a portion of it, as you also derive a private benefit from having a car on the road.
You might want to consider whether the terms of your contract are being adhered to, including any possible implied term that travel expenses reflect the true cost of travel. You may be able to refer the matter to a rights commissioner, or take an action through the Employment Appeals Tribunal.
It might come to the point where you would want to consider refusing to travel until the matter is resolved satisfactorily. If you were sacked because of this, and this was unreasonable, then you would be less likely to be disqualified from Jobseekers, and you may have a case for unfair dismissal.
If you are a member of a Union then speak to them about what action is possible. If not, then consider joining one.
If you do leave and it is considered unreasonable, the maximum disqualification is 9 weeks. However you do also have to satisfy Genuinely Seeking Work criteria. It may be that they could take the view that you are being too fussy about your terms and conditions of employment and refuse you a payment on these grounds. Unfortunately, the fact that working costs money is not a reasonable excuse in the eyes of the Department for someone to go on to the dole.
None of this would not affect your OPFP of course. Also, if you are working more than 19 hours, then consider Family Income Supplement.